How feasible is it to use a Standby switch to open/close the rectifier tube filament circuit?
Without the filament heating up the cathode, there'd be no tube current in the rectifier and so there won't be any high tension voltage at the B+/cathode. The rectifier plates would be oscillating at high VAC, but this won't do anything.
Then you flick the filament current on and there'd be a surge of current through the low resistance of the cold filament (which won't result in any rectifier tube current yet because the filament is still too cold). So I don't see any problem there.
If it's an indirectly heated cathode, there's no VAC seen by the B+ reservoir cap until the cathode is hot enough to emit electrons (which takes a few seconds).
With a directly-heated cathode, while the filament heats up, there'd be a small window of time when the rectifier cathode/B+ is between 0 and 5VAC - before the B+ voltage rapidly increases. I doubt this would affect the integrity of the reservoir cap much, because by comparison, in tube-rectified amps where a standby switch is between the rectifier and the 1st filter cap, the rectifier plates and cathode would be at VAC when the mains power is on, and there'd be a (tiny) period of time after the standby switch is on (before the B+ voltage rapidly increases) where the reservoir cap is subject to between 0 and 5VAC. So this would be no different to having a directly-heated cathode sans filament current, then turning it on.
In short, I can't think of anything that is deeply flawed about this idea. But I may have missed something