In theory you could maybe charge a supercapacitor over time with the power from NFC and then perform the update but you're looking at at least 15x (50mW vs 750m

In theory you could maybe charge a supercapacitor over time with the power from NFC and then perform the update but you're looking at at least 15x (50mW vs 750mW average update draw) the update time standing there holding the phone to the display while you trickle power over that connection. In reality with losses and extra draws to manage the screen you might not break net positive on the energy from the phone or you'd be looking at a 30-50x multiple instead of /just/ 15x.