How about standardising around second factor authentication with cell phones? Simple and easy. There are issues with losing the phone, but as long as there are

How about standardising around second factor authentication with cell phones? Simple and easy. There are issues with losing the phone, but as long as there are ways to lock an account, or alternate second factors. The FIDO standards suggest second factor auth (U2F, iirc) but with a 'device' (like a USB dongle). I tend to think phones are a pretty ubiquitous approach. And the more this technique is used the more likely there will be OS extensions that automate the process, for mobile browsing. Are there known defeaters I'm not aware of for this?