Many do, but the key is that the mobile apps generally only require access to 2FA for registration, so if they implement the mobile app interface they can get away with having users use the 2FA device once.

This is the case for Barclays, for example, where in fact once the mobile app is registered, that can be used as a Pinsentry (2FA) device replacement.

I'm in no position to answer authoritatively, but for what its worth the three accounts I have left in the UK, with different banks, can all be accessed without a 2 factor device.