> only needs to be a 2 watt
At start-up, the first cap comes to (say) 400V very quickly due to high current available from PT, the second cap starts from zero and charges through (say) 250 ohms.
So at that first instant the power dissipation is 640 Watts !! (400V in 250 ohms.)
The second cap will be largely charged-up within 0.01 seconds. That's actually fast enough to shave the apparent 640 Watts, but the math is tedious. There's also PT resistance.
Duncan PSU shows:
Peak of 293V 1.33A or 390 Watts near 0.05 seconds after turn-on.
RMS-averaged over first 0.1 seconds, 86V 0.34A RMS or 29 Watts. Over first second, 4.6 Watts. Over first 10 seconds, 2.15 Watts.
Yes, resistors will take short-term overloads. But the spec is usually 10X, not 390/2 or 200X.
If you ever had these filter resistors blow "for no reason?", that's why. Smack a 2W with 390 Watts for an instant, it doesn't smoke, but it gets micro-cracks. Do it 2 or 20 or 200 times, the crack goes right through and it quits.
_39W_ is the for-sure safe size. However we know from experience that the 10X spec is conservative. Basically we don't turn-on as often as some industrial punch which might apply thousands of overloads an hour 9-5 M-F.
Even long-term you have 1.9 Watts. A 2W part is going to fail.