On most amps a standby switch is unnecessary.
When valves ruled the world no other electronic devices using receiving valves (TVs, wireless sets etc), had standby switches.
Fender started to use standby switches in the late 50s. In my view this was to a) protect the filter caps from over voltage, and b) prevent arcing in DC coupled cathode followers - the standby switch very quickly appeared after the first Fender models with a DC coupled CF appeared in 1956.
Cathode stripping simply doesn't happen at the voltages found in valve amps.
As most other manufacturers followed Fender's lead standby switches are now seen as a standard feature (and I think you would trouble selling an amp without one).
Perversely, adding a standby switch has, in my view, caused reliability issues in some amps, eg the VOX AC30CC. The original AC30s did not have a standby switch, and as they have a valve rectifier the HT came up slowly as the rectifier warmed up limiting in rush current.
In the AC30 CC using the standby switch before energising the HT lets the filament of the valve rectifier warm up so that the rectifier experiences significant in rush current, which can and does cause the rectifier to short out.
I've seen several AC30CC with shorted rectifiers, and whilst I suspect that modern rectifier valves aren't that robust, this is a fault I rarely see in 60's AC30s and Selmers which use a valve rec with no standby switch.