iOS has a system-level interface for password managers so that the passwords are accessed without using the pasteboard.

Which isn't foolproof. I just tried to change my Apple ID password[1], and the password manager will only auto-fill the password field, not the verify password field, even if you invoke it with the cursor in the verify field. The only option is to copy and paste the password (or manually copy a 64 character password).

[1] I'm fairly sure I've copy-and-pasted my Apple ID password recently - I had to reauthorise my Apple ID (I think I was changing payment details), and there was no option to use the password manager (might be pre-iOS 13, so I'm not sure if that's still the case).

This doesn’t work everywhere; there’s been more than one occasion that I’ve had to copy/paste a password out of Settings because the system hasn’t detected a password field or gives me incorrect suggestions.

when that works... pretty sure the fallback is to copy/paste, unless copy/paste from password manager apps also bypasses the clipboard

Also, once you’ve got a password manager installed, it tends to get used for more things than just passwords. iOS’s non clipboard password/login doesn’t help me any when I’m copy pasting, say, my bank details from a secure note in 1Password.