If only the Tesla used NFC, or even bluetooth, for this purpose. As it is, leaving the fob at home is a huge risk because the app requires both the phone and car to have good cellular connectivity back to Tesla's servers. just not reliable enough. I'd love to see a phone based solution that could work directly to the car instead!
The range of NFC is too short to just leave it in your pocket. You'd have to take it out and place it within a few inches of the receiver on the windshield, or some other location where a receiver would need to be installed such as the handle.
NFC is an RFID standard and there are other RFID standards that have greater range, but are not supported by phones. So, for the purpose of supporting a direct phone connection to unlock/drive, Bluetooth is really the only practical option. However, my only concern would be reduced wireless security.
While I'm all for better wireless keys, I personally don't have an issue with the fob. I keep it with my wallet so I don't forget either when I go out. Sometimes it gets in a tight spot in my pocket and I'm afraid of buttons being pressed, though so far that hasn't gone beyond just being an occasional concern.