At least in Asia, there are a huge number of so-called unstudied texts. That can either mean actually truly unstudied, or simply unstudied in English.

One of the most significant sources of these in China are the local Gazeteers (usually called zhi 志). These are accounts, usually on the county level, of the goings on of the area. They became much more important and common in the 19th century, and there was a huge push by the Qing to further encourage patriotism by encouraging the study of the empire starting at the local level. Many of these that have survived the years have done so locked away in archives or libraries or private collections, and most have been inaccessible until recently, if at all. They are incredibly important for what they can tell of outside of official histories, but they're still mostly not something you can access.

Language proficiency is a pretty significant issue. It takes a lot of work to be able to read and interpret a lot of what has been recorded in the world, and for the English speaking world, that means a lot of the rest of the world's history has huge chunks which are inaccessible. Even if you read the language, getting access is an entirely different matter depending on the subject and the place where they are stored.

If you ever hear anyone say something about the sum of all human knowledge being available on the internet, you can be confident that that is very far from the truth.

Consider that most organisations, most companies, most political institutions, educational institutes, etc all have their own archives. Then there's personal archives of private citizens, which do get donated from time to time. Most of them haven't been studied yet - in large parts because many of them aren't very relevant to the subjects people tend to study. It doesn't even have to be new archives, really. Existing archives can grow as well as the result of donations, new discoveries, etc.

I personally did my research for my thesis in a recently unlocked archive that nobody had really studied yet. It was the archive of a newspaper, combined with the personal archive of one of its most prominent editors. It wasn't anything special and I doubt it'll get a lot of future research, but it just happened to fit really well with the research I was doing. I think that's the case for a lot of archives, really.

Even for relatively well-trodden, modern subjects there is always scope for new discoveries. To take just the most obvious example, many official records are kept secret for varying lengths of time (sometimes a century or more), so there is always new archival material being made public. Even outside this ongoing process, there is room for discovery. For instance, during my PhD I found some bundles of documents that had been originally miscatalogued by the archivists and had therefore never been accessed by historians before. That's without even touching on material in private collections (from private libraries to forgotten boxes of letters sitting in attics) that has never been properly catalogued and to which historians have limited or no access.

This doesn't, of course, mean that there are going to be useful unstudied texts on any given subject, so in that respect it's not surprising to see certain material crop up again and again in scholarship. Finding new material is only one facet of producing original scholarship.

To address the specific example you bring up, one reason that these sources continually reappear is because they exist in published format. One doesn't need to go to an archive to read Evliya Çelebi or Katib Çelebi, one simply needs access to a university library or even just the internet. Of course, the reason they are published in the first place is because they are seen as having universal value for the historian. Major chronicles are an essential starting point for any political history of the empire and therefore attract a great deal of attention and most histories have to engage with their interpretive framework to at some degree. They're also limited in number. In my own research I'm drawing on eight or so chronicles, representing basically all that exists (so far as I'm aware) for the mid-seventeenth century, all of which were either published in one form or another or had been edited by scholars at Turkish universities. In contrast, actual archival documents, such as imperial orders, financial registers, or judicial sicills exist in huge numbers and have only limited use for those who are not working on a narrow relevant topic. Examples of these are sometimes published in collections but it would be impractical to do so systematically, the material is just too vast. Scholars who are drawing on new materials for early modern Ottoman history typically do so either using these archival materials, or else the many un- or under-studied literary works housed in manuscript libraries around the Middle East, though above all Istanbul. They do this alongside previously published primary sources such as the above-mentioned chronicles.

As for why these specific chronicles get used over the others - Katib Çelebi and Naima have the advantage of being both chronologically comprehensive and highly detailed. Given how derivative Ottoman works of this nature are, it may seem redundant or an inefficient use of time to many historians to work with shorter, less-detailed works which ultimately don't differ much from what KÇ/Naima says anyway. I personally disapprove of this and think there's much value in exploring their nuances, but a KÇ/Naima and for later decades Silahdar/Defterdar-heavy approach does seem to be fairly common. Evliya Çelebi, on the other hand, is a totally unique source as a highly detailed on-the-ground first-person narrative of an Ottoman traveler, so he attracts a great deal of attention.

I recently read an interview with a prominent Hungarian historian who deals with XX. century history. She described quite in detail about how hard is it to access Russian archives for non-Russians. Archives that belong to the Defense Ministry and FSB are completely inaccesible making research into soviet foreign and internal affairs very incomplete. Then there are absolutely silly policies, like Foreign Ministry archives only allow 50 pages released per year, or another archive dealing with modern history limits foreign researchers to 100 pages/year requested and any copying needs additional permissions costing 3 euro per(!) page.

Sometimes they open up dossiers only to make them restricted a few years later, forcing research projects to stall or be dropped. And lots of decisions to release papers hangson single individuals who might decide on whim or based on personal relations.

To highlight a couple things, the fate of Axis soldiers who went mia or pow and didn't return is full of blank pages, we don't know the exact background proceedings behind many Soviet decisions, we don't know much about NKVD and KGB operations in the Eastern Block. And to take a huge step back in time, pretty much all Hungarian prehistory happened in what was the USSR, and Hungarian historians simply don't know how much potentially Magyar pre-1991 finds are there lying in some museums and storages.

With regards to official archives, in the absence of legislation like the American FOIA or systematic and scheduled de-classification, historians actually have the issue of not knowing what we don’t know is out there in the archives.