I know that it allows you to put any books you like on it if you jailbreak it, but I'm not really sure where else I can buy ebooks and the money goes to the author.
Also I actually quite like the default reading experience (I have a paperwhite) and jailbroken stuff often has less polish.
You can install a much better reader (such as KOReader), any software you want (games and the like), and remove all calls to amazon servers - the later being especially useful if you buy the cheaper, ad-supported Kindle; allowing you to remove all ads.
You can call Amazon or contact customer support and just act like a dumb boomer who doesn't get tech and they'll remove the ads for you, just ignore them when they explain why they're there and keep saying stuff like "I don't understand what this is for I don't want this on my screen please remove it grandson"
The device will still call home though; which sucks in terms of privacy and also allows amazon to potentially delete your books remotely.
you can’t jailbreak some kindles depending on their OS version
You can by opening them and connecting to an UART port; it's slightly more complex to do though.
You can still pirate books without jail breaking, you can send any pdf file to your kindle.
It doesn't hurt the e-ink display at all. I've had my 1st gen paperwhite running android for years.
I can play sudoku and scrabble on it now, that's the best part.
You can also add books by setting up an email address for the kindle on the amazon site and then sending PDFs to it directly. Some other formats also work.
Only problem is finding a source for the books.