>why should one assume that the various keyboard apps in the App Store aren't keyloggers trying to steal my login info?

Honestly, you shouldn't.

Theoretically, Apple + Google take a % of all payments that go through their store, with the expressed reason being to "monitor and police the safety of the apps on the app store". You really should be able to trust apps on the official app stores, but I don't trust Apple or Google, so the whole system is moot I guess