The convenience is that people don’t drop their phone in the toilet and suddenly lose access to all of their accounts.
Google took forever before adding cloud-sync to their TOTP app even though pretty much all the other ones did it from day 1. And I bet a non-trivial amount of people got locked out of their accounts because they hadn't reliably stored recovery codes.
Financial services are actually the least of your worries since you can get ahold of customer service and eventually recover your credentials even if it takes a few days and some snail mail. However if you lose access to Gmail or Facebook, good luck unless you know an employee.
Yeah, I do. Do you? Because it's certainly not what you're implying