It would stop you from using the email sideload option, which is my favourite way to get books on. But you could turn WiFi on just for that and off again. More of an issue would be sync with the Kindle app, say on your phone. So if you don't take it everywhere but find yourself stuck and wanting to carry on reading, you can get your phone out and pick up where you left off. Honestly, that's pretty handy. But everyone's use case is different.

Wikipedia won't work. It'll nag you about how you are not synced to the cloud. Every single time you go back from reading to the library page. Very annoying, but something I think better tolerate than to have yet another telemetry stuff in my life.