I believe the Standby switch was invented so that you could mute a noisy amp when you weren't playing it, and quickly unmute it when you wanted to.
It otherwise serves little purpose.
There are plenty of ways of muting a valve amp without resorting to switching the DC HT - a muting switch on the input would take most noise out, as would shorting the output (something you can do on a valve amp of course, it's open circuit that they hate). I think it was a brainless design decision, probably done on the fly when a musician flagged it on an early model.
Edit:
In fact, I have read on several occasions it is a popular myth that the Standby Switch is there to prevent "cathode stripping", but the reality is that only very high voltage transmitter tubes suffer from this.
Is this a thing?
Cathode stripping is caused by pulling so many electrons out of the cathode that it loses its space charge and is exposed to ion bombardment. It's certainly a thing in
high voltage tubes where full HT is applied while the heater is still warming up. It's debatable (and frequently debated!) whether this is a factor down as low as 450V - at a few kV it certainly is, but this is a 'danger zone' between where oxide coated cathodes are still useable and where they transition to thorated or pure tungsten cathodes (
big industrial or transmitting station tubes, X-ray tubes, Kenotrons etc. working at 10s of kV.
At the same time, suddenly hitting a hot amplifier with (over)full HT via the standby switch might hit the tube cathodes with a momentary over-current situation depending on the cathode / grid biassing arrangements, charging of coupling capacitors etc. That might count as stripping,
caused by the standby switch (and poor design).
What
is a thing is Cathode poisoning, where the tubes sit for extended periods with heaters running and no bias on them. This creates an insulating cathode interface layer under/over(?) the oxide coating that reduces its emission. That's the one I would be more concerned about with amplifiers accidentally sitting in standby for extended periods. [Edit: this used to be a
real problem in so called 'quick start' valve TVs until they learned and started reducing the heater voltages too ('slightly slower start'?)]