Apple ID problem: sharing iTunes Apple ID in two factor world means authentication requests go to one of many possible devices

In the old days, before family sharing, families shared purchases by sharing an iTunes Apple ID while using their own Apple ID for me.com services.

Now that we've moved to 2FA for iTunes Apple ID there's a new problem with this.

Authentication requests go to one of the devices that uses that shared iTunes Apple ID. Just one. Usually the wrong one.