You picked 2-of-3 because it sounded balanced. The cryptography will honor any k of n forever — the question is whether your team can. Work the people math before you enable anything: with a quorum of two and three administrators, one resignation leaves two — a proposer and one approver, still exactly workable, with zero slack. The next loss strands every gated change, including the one that would have fixed it. That is the arithmetic behind the people + 1 enable rule from the last frames — and it does not stop applying after you click enable.
The trap has a direction. Once the control is on, creating an identity is itself a gated change — so adding the administrator who restores your margin takes a quorum, which means the repair only works while you still have one. Propose the replacement the day the first person resigns, not the day the second one does; after that, it is too late by construction. Vacations are gentler but not free: the asynchronous design lets an approver act days later from their own session, yet requests do expire — control-switch proposals after 24 hours, intercepted changes after 7 days — so with the roster at zero slack, one absent approver can quietly time your change out. And remember the vote math cuts both ways: a request dies when as many people refuse as would have been needed to agree, so at 2-of-3 a single rejection kills it. Head-counts, not signatures, are what you are really configuring.
Break-glass cards are the same shape drawn on paper. A 2-of-3 set tolerates losing one card; lose a second and what remains reconstructs nothing — and there is no reprint. Replacing a lost card means generating a whole new set, which retires every card already printed, and with approval on, generation is itself a quorum action. One asymmetry works in your favor: a lost authenticator is recoverable even below quorum — the password plus k cards restores that administrator's own login and refills the roster. A departure is not. Only spare people cover people.
Now I can pick a quorum my team can survive, not just admire.