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A backup second factor is not very likely to be useful to an opportunist. Is they a reason to not just store it at home, perhaps in a fire resistant safe?

[subb]

Mmm maybe. A bit annoying to backup regularly, but maybe by doing an hybrid approach like other have suggested here could help reduce the backup frequency/annoyance, i.e. duplicated two-factor key for important accounts, and the rest is stored in a password manager.

Now if only banks would implement proper two-factors...