It's not so much that those docs haven't been read, but that they haven't been read in a particular way or for a particular academic purpose.

Take for example Patrick Wyman from the fantastic Fall of the Roman Empire and Tides of History podcast. His dissertation was on the thousands of letter that have survived from the late Roman Empire, a process that took him 5 years. But as he describes in detail in episode 13 of the Fall of the Roman Empire, he didnt just read them for their content, but also mapped their journey from sender to receiver and was therefore able to use that map to trace the ebbed and flow of Roman borders, trade, and social connections as the empire fell apart. He could do this because he was steeped in the current literature surrounding those text and was able to put them in context to piece together how and why those letters moved how they did.

Unfortunately it is unlikely that you could make a substantive discovery by causally reading as a layman. You'd need the training of a professional history as well as an understanding of the past and current academic consensuses on the time period and subject matter you are reading to be able to figure out if a text is of particular significance or to link texts into supporting a coherent theory. Itd be like trying to contribute to geology by walking around looking at every rock in your path. Sure there might be a chance you find something interesting, but more likely if you did read something of historical significance you would have no idea of its importance and would just move onto the next doc.

There is an exceptional database of digitized texts connected to the University of Michigan library - Early English Books Online. It goes from about 1400 to 1700. There is also a modern text transcription for most of the texts, which can be very helpful if you haven’t trained in reading Renaissance writing.

You may need access to a university library that subscribes to it, because most city libraries won’t. You can also subscribe to it as an individual, but I don’t know the cost off the top of my head.

Sure, but they’re mostly in databases.

For example for my scholarly work I look at petitions written by poor women to monarchs that haven’t ever been touched by historians but tell you LOADS about the period. It’s all about finding what’s slipped through the gaps, and learning how to interpret it so that the importance is properly understood.

It seems to me that just turning books into useful databases and spreadsheets would do the most aid.

You could literally just write down every event in a book in excel and release that publicly to aid everyone who wants to examine the time period without having to read hundreds of lines of irrelevant detail

Are you a student, or do you have access to EEBO/HathiTrust?

https://www.zooniverse.org/projects has a variety of crowdsourcing projects of various provenance, some of which involve historical documents. The History tab will perhaps be of most interest to you. Here's a few select projects:

https://www.shakespearesworld.org/ asks you to help transcribe handwritten Elizabethan documents.

https://anno.tate.org.uk/ is similar but for documents in the Tate's collection of documents from and about artists.

https://www.antislaverymanuscripts.org/ turns handwritten correspondence between anti-slavery activists in the 19th century into digital text.