I think it is hard to say actually. An account that gets killed off by 2FA failures is dead, which is definitely extremely annoying. But on the other hand — the maximum cost that could be incurred is just the value of the account, and lots of our accounts are actually basically valueless (Facebook, Twitter).
On the other hand if your account is taken over, it could be used to perpetuate scams (which could harm your loved ones if they fall for the scams), it could be used for various things that might hurt your reputation. Or depending on the type of account it might be a stepping stone to get into, I dunno, your bill-paying account for some utility company, which will probably have all your bank account details in there because utilities companies tend to not be super on the ball about that kind of thing.
On the other hand if your account is taken over, it could be used to perpetuate scams (which could harm your loved ones if they fall for the scams), it could be used for various things that might hurt your reputation. Or depending on the type of account it might be a stepping stone to get into, I dunno, your bill-paying account for some utility company, which will probably have all your bank account details in there because utilities companies tend to not be super on the ball about that kind of thing.