What mistake is a user making? Sophisticated users lose access to their 2FA credentials all the time. The conventional advice is "enroll multiple TOTP devices". Most users don't have multiple mobile devices to enroll. Now you're asking them to enroll something on the desktop, which effectively undoes the "something you have" benefit of TOTP (see: the 1Password thread above). At least a recovery code _can_ be printed out.

I don't think the logic you're employing here is coherent. Consider it a bit longer! This post could be a good longstanding reference, but this is a big flaw.