The way I think about this question is that it's a matter of 'live' versus 'dead' history. It's not a matter of time, necessarily, but a function of how much people today still passionately care about a subject, how far it affects people's lives in a way that feels tangible and real to them. The American Civil War might be an example of 'live' history which falls beyond 100-year margins. This is a subjective measure of course - I'm sure we could find people who are still really, really upset about the collapse of the Roman Empire - but subjectivity is kind of the whole point here.

I personally specialise in an area of history which, for certain people at least, is very much 'live'. People care passionately about the Spanish Civil War, inside and outside of Spain, despite the many decades which have passed and the deaths of most actual participants. For those on the left, the people I study are still venerated as heroes for making a stand against fascism. This inevitably colours what I and other scholars write about the subject - we are implicitly or explicitly reacting to partisanship, participants in a debate framed by inherently political questions. I have close to zero personal connection to the conflict. It didn't affect me, my family or my country of birth directly. I could, if I wanted, make some claim to neutrality, embrace my perspective as distant, objective and able to best make informed, rational decisions. Yet even then, I cannot pretend to be a neutral participant in these discussions - I have my own views, my own politics, and beyond that, the questions I am asking of the past are shaped by what other people have asked before, and the record that has been preserved through human agency.

Even beyond that though, if I tried to divorce my subject matter from the passion it inspired at the time and ever since, I reduce my ability to understand it. To understand history, we often need to understand more, rather than less, of the emotions of the past. We need to be able to empathise, to understand, to try and get inside the heads of the people we study. We can never do this perfectly, thanks to the limitations of the historical record and our limits as human beings. But without even trying, we can't hope to better understand the past. Unless we get bound up in emotions and subjectivity, we make history infinitely more shallow. Past a certain, very basic point, all we have is interpretation, based on limited evidence. In fact, in this sense recent history is actually easier, as the historical record is much better preserved, and covers a much wider range of voices. But that still doesn't make it neutral.

The inevitability of the situation I find myself in here has long been acknowledged in historical methodology. There is no vantage point in the present through which we can perfectly and objectively understand the past. How we view the past - whether last week or last millenium - is inextricably bound up in who we are. Moreover, the historical record itself is not not neutral - what has been preserved is not only the function of what people at the time thought was 'worth' preserving, but what subsequent generations have deemed worth keeping. Subjective, political, even polemical approaches to the historical record have all helped reveal more about the past, even if they neither aimed at nor achieved objective historical truth. Objectivity, therefore, isn't the primary goal of historians today - the objective is to understand more about the past, in the knowledge that we will never be able to grasp everything. For example, if you ever ask for a 'definitive' or 'objective' historical account of an event or period on this subreddit, you'll never get a recommendation for just one text. You'll get at least several, representing a series of interpretations and perspectives on the past, because even for history thousands of years in the past, there's no single, neutral interpretation.

Even beyond forsaking especial claims to neutrality or objectivity though, there's another very good reason why we study 'live' history: because it matters. Live history is what drives our lives today, on individual, societal and even global levels. We need to better understand it precisely because it's alive, and potent. While we need to acknowledge that our efforts are imperfect, and we might not ever manage to figure it out completely, the alternative is much, much worse when the stakes can be so high.

I think before I get to the meat of your question, I'd like to point out and discuss a couple of things:

1. As discussed in numerous locations around this sub, the study of history does not necessitate a lack of distance or an "impersonal approach." Not only can passion and interest influence your work in a good way (you wouldn't be writing about a subject in the first place if you weren't interested in it, and you want the people reading your work to be interested in the subject as well), the concept of "an unbiased study of history" is often incredibly difficult if not outright impossible in a lot of cases; historical records are incomplete or inaccurate, or they're written by individuals with their own beliefs, agendas, and personal biases, or only certain things are kept via the record. If modern historians are working with an incomplete, inaccurate, or purposefully altered historical record, historical analysis will be similarly colored despite their best efforts otherwise. The past century and the present day is no different than the past in that regard, to be quite honest.
2. Thoroughness via impartiality (which is actually what you're describing), aka "not taking sides, giving equal value and weight to both or all sides of an academic argument/discussion" is not nearly as important in the general academic sphere as objectivity, which is "how do we look past our personal biases and our personal experiences of something we may have actually experienced and look at what facts we have." Even then, there's a lot of nuance in how to look at the facts that we have on a subject, because historical analysis is inherently interpretation of the historical record, and interpretation comes from active, conscious decisions that historians make on a matter.
   1. The way historians interact with and write about history, whether that be "living" history or history long happened, is inherently influenced by their own personal upbringings, politics, education, and interaction with other historians, the sources they choose to use or have the ability to access, and the thoroughness of the historical record itself. This is a personal opinion and not an academic one, but I would go so far as to say there is no 'unbiased' or 'objective' interpretation of history beyond "this event happened on this date" types of issues. It's simply not possible. To study history is to study humanity, and humans are not objective, unbiased creatures; it is impossible to thoroughly study history without acknowledging and making room for the inherent subjectivity of the human beings that lived it. This is reflected in the changing nature of the historical academic sphere, where "explicitly stated and carefully controlled subjectivity" has become the name of the game in recent years due to the concept of authors honestly stating and explicitly working with their biases being seen as a more honest and productive way of dealing with historical analysis than the pretense of a "detached analytical antipathy" that simply doesn't exist 99.9% of the time.
3. While the "lived" history of the modern era still reflect and influence our way of thinking, you must remember that the thinking of eras past does as well. Western (and specifically European) society is still shaped in enormous ways by Ancient Greek and Roman society, with their societal, political, and economic structures (not to mention their philosophies) still influencing how modern society operates; you see a similar parallel with Enlightenment-era politicians, philosophers, economists, and thinkers. How long ago "history" happened has no bearing on the amount of influence the event/situation may or may not have on the present in its sphere of influence. An event that happened ten years ago could have just as much influence on the state of things today as an event 150 years ago; you need to take both into account for a full and accurate historical picture. For example, you could make a solid case that the French Revolution of the 1790s and the post-WWII restructuring of French society are relatively equal contributors to the structure of modern French society; one happened 250 years ago, the other happened 75 years ago. The past influences the present; it doesn't matter whether that past is yesterday or 200 years ago.

Now, onto the core of your question: as someone who has a field of specialty in a field that is less than 100 years old (American comic book history, specifically superhero comics), studying a field that is largely modern history is a fascinating exercise in watching how history is created, formulated, written, and thought about in the academic sphere as it is happening. Questions like "how do we chronicle this history?" and "what is important to save, collect, and discuss?" and "who/what were the most important foundational influences in this field?" are things that are actively being discussed! And in terms of that, modern history actually has a massive leg up on people trying to study this stuff in say...the 1950s, because we have the benefit of perspective, technological advances, and a much richer historical narrative to work with! I have the ability to access a random Golden Age Wonder Woman comic at literally any point in order to analyze how William Marston portrayed real-life feminist activist figures, for example! Modern historians studying recent history have the benefit of technological advances that allow for much easier storage and distribution of history, so they have a much more complete and accurate historical record to work with and analyze.

Because comics are a cultural byproduct and a form of literature, there is a lot of social discourse in comics and the history of comic creation that reflects the historical, political, cultural, and economic events that are happening at the same time the comics are written and distributed. Comics, as pieces of literature, are inherently subjective interpretations of history and cultural events (past and present); in this way, they provide an interesting avenue through which to view history...even recent history. Chronicling the rise of Sam Wilson as Captain America and his importance as a black man taking the mantle of "Captain America" is just as important as tackling the social issues that led Joe Simon and Jack Kirby to create Captain America in the first place. But "the truth" is no easier to parse for the latter just because it happened long before I was born....it's just different, and the perspective you take towards each issue is different. The full effects of Sam Wilson becoming Captain America may not be fully realized yet, but you still have the ability to analyze how his stepping into the role of a legacy hero has changed how people perceive his character, or how he was received by the general Marvel readership when he took on the mantle.

Those things are often actually easier to study in the moment, because you are quite literally living it as it happens. And when studying things like that are well...inherently subjective experiences, I feel attempts at "impartiality" can actually detract from a greater "truth" and a fuller historical picture, because the feelings and emotions around an experience are vital aspects of how that experience will eventually be told in the historical record! We remember the horror of the Holocaust via the incredibly emotional and visceral testimonials of its victims and the calmly detached or emotionally fanatical records of its perpetrators. We often talk about World War I via either the larger-than-life leadership personalities of the time or the horrors of trench warfare. Emotion or subjectivity in historical analysis isn't bad. What's "bad" is letting your emotions cloud your anlaysis to the point where you are creating bad analysis or actively ignoring things that don't fit your perspective because you are trying to fit history into a box you created for it and refuse to allow it to leave. And I think that's no easier or harder when you're working with recent history than when you're working with history that happened long ago, because that's a problem of perspective and not a function of what type of history you're looking at.

Here are links to a few other threads about objectivity in historiography:

• How important is objectivity in academic historical works? answer by /u/restricteddata
• Objective History answer by /u/Bodark43
• As historians, how do you recognise and avoid biases that will have formed due to the culture and environment that you grew up and live in? How do you avoid under/overcompensating? answers by /u/commiespaceinvader /u/Snapshot52 and /u/restricteddata (again)
• What are your thoughts on the 'objectivity' question? answer by /u/CrossyNZ

There are quite a few more if you search through the subreddit's archives. It's a fairly commonly discussed topic.

You might also find Monday Methods: Understanding contemporary concepts from different perspectives - An Indigenous view of technology, science, and history and Theory Thursday | Objectivity relevant.