It’s just when I recommend a book. I was so delighted when I discovered the library actually acquires books based on recommendations, I do it all the time now! However, there’s no way to indicate what format you’d like to have the ebook in. Yet.
Can’t you use Calibre to convert from ePub to the kindle format?
Assuming DRM is not a problem, you should be able to. I’ve done Kindle (aka .mobi) to ePub quite a few times, and am not aware of any reason the reverse shouldn’t be equally doable.
I assume the Overdrive format does block conversion, or else everyone would just keep their borrowed books.
One good thing from having digital books: Much harder to be burned by zealots.
One bad thing about digital books: Much harder to burn books if you need a fire 
I don’t know, but I’ll find out in the next week and let you all know!
I don’t want to keep my borrowed books. I don’t want to steal from authors. If I love a book, I’ll buy it, just as I always have. I’d just like to have access to all the library’s ebooks, just like I have access to their physical books.
I don’t know if format-shifting (and/or DRM removal) is legal where you live, but if it is, you can use free tools to strip the DRM and convert to another format freely. There’s even a simple Calibre plugin on that page which makes it super easy to do. Of course, don’t use it to steal books… delete it when your check-out period is up or buy the book.
I still don’t understand the OP’s gripe.
My gripe is that in principle books in electronic format could be lent out to any number of library users, for the limited period; but instead the library can only let so many people have copies at a time, which means availability is no better, and often worse, than print books.