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Installing software that functionally doubles as a keystroke logger has always sketched me out enough to never try.

This is ignorant of how keyboard apps work on iOS. By default, they do not get internet or even network access, unless you explicitly permit it.

Can you prove that?

If you don't trust Apple to enforce that, can you even prove that Apple won't act as a key logger too?

If you are that suspicious of Apple you should not be using iOS at all.