While not cryptographic level auditing, this is arguably a UX feature for sites to implement -- on their inevitable loading spinner after login, they could show you the U2F tokens enrolled, and their most recent use on a small timeline. If your cold backup suddenly goes from ancient to now, that ought to be looked into!

Regards habits, I find U2F is so easy to use that there's no real issue there. The bigger issue is that (relatively) few services support it. I'd much prefer to use it over TOTP phone generated codes, but far more sites seem to support phone app generated codes (while pretending you need their proprietary app to use them, even when it's just plain TOTP) or, even worse, SMS!