This is a crazy problem. Even Apple requires you to use SMS 2FA, and does not let you opt out or use any alternatives.
My employer uses this as well and I was locked out (couldn't do any work) for an entire day because their SMS messages were not being delivered.
As a side note, Apple is also the only platform I've ever used that requires you to type your password in without seeing it, which makes using an actually-secure-password really fucking difficult.