This needs to be rethought totally. To the point where it always lets you use the phone for these passwords and lets you flip to another app and copy/paste things in.
Apps can be worked around where they have a code and are activated elsewhere. The Apple ID case, needs handling if we are going to be prompted over and over. I've had to do it three times now and if that's all, okay (initial, App Store, and iTunes preorder. I set 'never ask' for purchases).
I have a roommate and we both have Apple IDs/accounts (naturally), and the best feature was the Remote app for entering passwords discretely. Neither of us would make purchases on the others' accounts, but I don't exactly want things displayed as a I type (sort of like the people that refuse to use TouchID and enter in a 4-digit pin with no regard to those around them).