I say this as a Tesla owner...
Do not leave your keycard at home. Every Tesla owner should have a keycard in their wallet (You don't go driving without your wallet, do you?). You never know if your phone will die.
It's the same with cars that use keyless start. In my wife's Honda CRV, the fob has a physical key that can be removed to open the door, and the Start button can read the RFID in the fob if the fob battery is dead.