I have multiple devices with lithium batteries plugged in 24/7. A kindle that I use as a display for example. So far nothing exploded. If exploding kindles were a thing I guess I would have heard.
I have not had anything explode, but I have had Macbook batteries expand on me on two separate occasions to the point where the case was visibly warped. Both times I was away from home, so it was extremely inconvenient.
I flashed it. Don’t know if always on works with the browser. But jailbreaking is easy and I think even reversible. Then you can ssh into it and even setup a cron to download a picture and refresh the screen.