There is no problem running the filament directly from the AC mains as long as you can be sure that voltage between the filament and cathode can never go above 250V. The problem is not where the filament power comes from, it is the voltage difference between the filament and cathode that matters.
But now suppose the main supply (HT to the PL504) is on the secondary of a transformer and is floating at around half the AC value. The voltage between the filament and cathode will reach around 280V and you risk the insulation breaking down. Consider what might happen if you short circuit the AC mains directly to circuitry on the secondary side of the HT transformer, it could be dangerous and even lethal if you have external connections that can be touched.
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