Oh it's definitely possible at counter service restaurants like McDonald's, Panera, etc. However, I personally wouldn't want to have my server walk off with my phone, and having to go to the back with them just to use my phone to pay for something (vs. having them take my card as usual) eliminates a lot of the convenience.

(Yes, I know, we should really be adopting pay at the table like most other countries. Good luck with convincing American restaurants of that too, especially since tip adjust is still allowed and PIN isn't required on chip cards.)