The statement by Ramachandra Guha is extremely true for colonial Latin America. Most books and articles published on colonial Latin America these days rely on some combination of imperial archive work in Spain and local research in archives in the geographic area studied to produce the primary source base. Spain's archives have digitized some of their material, but it is hit or miss if those materials are relevant to your particular project. Local archives in Latin America are almost universally not digitized at all. If there is digitized material, it may only be select documents or might be documents that somehow ended up in the US or Europe and got digitized there.

Regarding your first, larger question, how relevant are archives and libraries nowadays, my answer here is it depends. There is not one way to "do" history research, and no project is the same. Your attachment to archives and libraries depends on what type of history you are doing, what time period you study, what materials you need to answer your research questions, and what materials archives/libraries for whatever reasons have digitized in the past. If your project can rely on only print sources from early modern England or Parliamentary papers, for example, you might be able to do the whole thing from home. Or maybe if you study like ancient Greece or some other project with a very small source base, where there are like twenty surviving sources that have all be in circulation for hundreds of years, maybe you can actually own copies of almost every source you're using (I'm exaggerating a little but there are projects that have tiny source bases like that!). Or maybe if it is a more twentieth century project, there's a good chance that a lot of what you need will be digitized already in some database. Or if you just happen to be working on a project with materials that have already been digitized by sheer luck. Or maybe you are relying on oral history, so you are actually talking to people or accessing their recorded voices online. Or if the archive you would like to work remains closed for political reasons, you might have to make due with what materials are available, like digitized newspapers, without relying on a particular restricted archive.

Yet archives and libraries remain the principal source for historical research because most of these conditions don't apply to everyone's individual project. Carrying out larger projects based on original research tends to require substantial on-site research. Even projects where a lot of the material is digitized, some of the important stuff that a person needs probably isn't digitized, which is why no one has researched your topic in the past. One might need to spend less time in the archives, but still some.

Also, many historians argue that there is an element of materiality to archival research that can get lost in the process of digitization. While this attitude might seem a bit cermudgeony for layman who consume podcasts, youtube content, and general popular histories, this is much truth to it. For example, sometimes there are marginal notes that get cut off when someone scans something or that you might overlook by not happening to look right at it. Sometimes being able to see the colors or touch the material or examine the construction of a document can provide historians important insights about the past. Sometimes the tactile nature of interaction with primary sources can generate questions. Sometimes the digitalization process was done so poorly that the stuff that is digitized is illegible anyway, so you have to work with the real thing. And sometimes, the primary source itself is so fragile, damaged, or delicate that it can't be put into a scanner without it being damaged in some way, so if you want to work with it, you have to do it in person.

I am very curious about what will happen as a result of COVID. On the one hand, historians have spent the last year finding work arounds for not having access to archives and libraries. Some libraries and archives, especially those with lots of financial resources, have been undertaking larger digitization projects than ever before to help out their users. Maybe the pandemic will lead to more access in the future or might influence a general cultural shift among historians away from our solitary work in lonely, dusty archives, towards wanting more digitized content and more collaboration. Plus, it isn't very hard for a lot of younger historians to imagine a world where most of the material is digitized and accessible in various databases capable of carrying out like...machine learning driven, GIS-driven, or big data driven projects. Or where all the material is text searchable, even materials that have been handwritten. But then again, history in academia grows less influential by the day as fewer people major in history and take advanced classes. Falling enrollments means cuts, fewer historians doing original research, and smaller audiences for boring monographs of original research. Budgets for smaller, local archives remain insufficient to carry out any digitalization at all, let alone create a completely digitized utopia of accessible historical content for the everyday lay historian, and many archives now will face budget cuts because of the global recession. So perhaps archives and libraries will remain the mainstay of historical research for a long, long time.

I can offer the perspective how archive material comes to be online available - and thats a long way.

I'm an archivist myself, so I'm going to concentrate on archives and digitization in the archive i'm working in, but I think most points are the same everywhere else. So archives are usually - depending on the kind of archive - in a situation of constantly receiving new material. This material must undergo some archival work like describing, cleaning, organizing. This takes time and only after that the archive documents might be digitized. But digitizing is an extremly time-consuming and expensive process. The documents must be scanned, a text recognition-software has to be applied (so the user is abled to search the document) and afterwards the document must be annotated, described, tagged and put online in the right categories (this is just the basic workflow, there are more steps possible, like transcriptions etc). Those steps must be done for every document and partly by humans and not a programme. To conclude: All these make it really expensive and a long term-project to digitize archives. Thats the reason why many documents arent avaible online and historians still have to search in archives. Additionally working in the archive itself offers some chances, like the direct contact to the archivist who might be able to help and online documents can be incorrect.

Even tough I didnt answer the question directly, I hope I've offered more understanding why digitizing archival documents is relativley slow.

Edit: grammar

I think you have had some very interesting answers already but I wanted to raise an additional few points. They come down to the same observation, that the importance of archives depends on the nature of the historians work.

It is useful, I think, first to understand the difference between popular history and research. Both are valuable and important but they do different things. In a blunt simplified way, popular history takes knowledge that specialists have and makes it available to a general public (AskHistorians is all about popular history in that sense). Research generates new knowledge. So they often have very different uses for archives.

A popular historical work might be satisfied with a relevant internet archive. A researcher would like to find something 'new' and one of the quickest ways to do that is to find a 'dark' archive which has not been previously tapped.

Sometimes of course people use both. I'll give you a practical example. Some years ago at the behest of the department I was then in I wrote a book on how money is represented in board games (www.amazon.co.uk/Playing-Money-Robert-Bracey/dp/1912667045/). It is very much a light popular history, covering ground that would be well known to a specialist in the history of gambling, fantasy literature, or insider trading regulation (games make an eclectic mix of connections). For the book I did make use of two archives - one online and one physical). The online archive was the oral history of the Security and Exchange Commission (http://www.sechistorical.org/museum/oral-histories/a-d/). These are fascinating documents because they give an insight into how SEC staff thought about the regulation they were creating in the 70s and 80s - but I used it for flavour. The argument that ethics rather than legality was the primary driver of regulation is one you could arrive at reading secondary sources by people who specialize in the history of that institution - it just connects dots between disparate histories (financial markets and a pop representation of those markets). On the other hand when I wrote about the way gambling is represented in games I did visit the physical archive for one of the game companies. And the result is that there are observations which no-one else had made before. In fact, one of the things I realised is that though there have been three fairly detailed histories of the game Monopoly, all of which have touched on the legal wrangles which have engulfed it over the years, all of those authors depended on archives in the United States. But for most people outside the US if they played Monopoly it would have been manufactured by the British company Waddingtons and the archives of that company (which are physical and unlikely to be digitised any time soon) contain a valuable perspective on the history which has not been adequately tapped (I'd highly recommend a visit for anyone researching that topic - I certainly didn't exhaust the potential).

So yes physical archives are still invaluable to most historians. Though, of course, that is not to diminish the importance of digital archives.

I want to make a point that digital archives have increasingly made possible types of research that simply couldn't be done in the past. Part of my research is numismatics. Within numismatics there is a very specialized form of research known as a die study (if you care an introductory lecture I gave ten years ago is available here https://youtu.be/_y1THkRvU3I ). It involves comparing hundreds, possibly thousands of coins with the same design. That used to mean laborious work visiting both museums that physically house the coins and also archives of auction catalogues (most coins are not in public collections). There is a major archive of catalogues in Cambridge in the UK, one in Greece, and a less complete one in New York - that is a lot of flights. But increasingly catalogues are digitized and its now possible to gather that data very quickly. Larger and more extensive studies are possible as a result.

You would be surprised what gets skipped over in an archive. There's an easy to fall into trap, the notion that just because it was scanned or sorted, means that its not new information. Far from it, I found the likely burial record of the pirate Anne Bonny on a digitized list of Jamaican burials. I wasn't the first, a local archivist had gone over that stuff in the late 80s. Hell, it was available through Familysearch, a Mormon version of Ancestory.com. Why they would have control over documents related to Church of England burial records is beyond me. Point is, sometimes you find a gem hiding in plain sight.