It's fine that the app on your phone can read your messages, for that reason. It's not fine that it can then send them to its developer or anyone else. (I know it claims it doesn't. My point is that it can, so you have to trust that the developer is telling the truth, and that an update will never make it start to.)

Isn't this because there's not a separate "internet access" permission?

iOS actually does have a separate "internet access" permission for apps, but it's only available for devices sold in China.

It's funny you mention it; I've been cobbling together this link collection the past few days and your comment has spurred me to finally publish it:

iOS: Disable WiFi (not just cellular) for specific apps without jailbreaking https://tinyapps.org/blog/202209100700_ios-disable-wifi-per-...

So it's not the case that it'd be too much work or technically infeasible for such a permission to be available to us. It's just that Apple doesn't actually care about us or our privacy.

Probably impacts ads too much

Thanks, we couldn't deduce this alleged reasoning by ourselves.

This must be a new take on the word "private".