>So we went to the settings app, searched for the email app entry, no dice. Eventually through trial and error, we discovered some obscure entry in the settings app to manage accounts. It makes no sense at all. Literally none.

It makes a lot of sense. iOS uses your Gmail credentials for more than just mail (it can also sync contacts, calendar items, and notes to your Google account). So it makes sense to not have it within the Mail app.

Besides, it's not "4 layers deep". It's directly under a top level Preferences heading called "Accounts & Passwords" in Preferences, which should be the first place to look for, well, Preferences.

Third, you could find it also by just typing "accounts", "gmail" etc on Spotlight search. Again, just a click away.

If that's the sort of "problem" iOS has, it's pretty solid.