I beg to differ....

You can differ all you want, but it doesn't change the facts:

Look at the supply current with the capacitor across R1:



Compare that to the supply current without the capacitor:

 

Bag the capacitor.

1) the thermal time constant of the filament is long- just make sure the PWM period is much shorter.

2) the inductance of the lamp is negligible, if you are concerned, place a reverse-biased diode across the lamp.

 

Bag the capacitor.

1) the thermal time constant of the filament is long- just make sure the PWM period is much shorter.

2) the inductance of the lamp is negligible, if you are concerned, place a reverse-biased diode across the lamp.

The default PWM rate for an Arduino is 500Hz. Lamps dim ok at 50Hz without putting capacitors across them...

The inductance of the filament is so low that it is not even on the radar.