The "standby switch" is a complicated yet simple device. Is it necessary? Maybe, for some designs and maybe not for others.
Historically, with tube rectifiers (especially indirectly heated), the tube structure's temperature ramped up via the heaters before the rectifier started conducting so the turn-on was soft(ish) and naturally delayed. The advantage of any type of delayed application of high voltage to the power tube is a more gradual expansion and thermal equilibrium. Perhaps you have heard power tubes make (mechanical) noise as they warm up, this is due to all the structures expanding when heating (and contracting when cooling).
The issue of potential cathode stripping is an interesting one, not really even a potential issue with tube rectifiers but possibly a problem using solid state rectifiers... especially when amps are turned on and off a lot.
I looked back into some of my historical documents, I haven't really thought about this for years, and looked at some of the Altec and Ampex power amps because they were designed for long lifespan and do not have standby switches. What is different about these is the conservative voltages that the power tubes are operated at, and in the case of the Ampex, the screens have their own supply that run about 60% of the plate voltage. Also, solid state rectifiers at those times (where solid state were used ) were selenium types which by nature are fairly squishy compared with silicon rectifiers commonly used today. All of these elements served to improve lifespan (at the tradeoff of reduced power), and it was not uncommon to see 5,000 to as much as 10,000 hours on a set of power tubes. This was important because theatre sound systems typically operated 10-12 hours/day, every day. Another aspect of such operation is the relatively small number of power-ups and downs over the tube's operating life.
With today's guitar amps operating at stupid-high plate voltages, and lots of power-up/down cycles, the argument for keeping the power tubes hot while swapping guitars, going on a short break, messing with pedal board wiring certainly makes for a compelling convenience. With capacitive buffering of the plate supply (or even better, a ramp-up circuit in the B+) this minimizes the step function of voltage on the plates.
Is it "necessary", probably not in the strictest sense, but it can be helpful under the conditions that SOME tube amps might see in the wild.
If I were to design a tube power amp today, I might consider more active management of the supplies... ramp-up/down of the B+ and maybe screen supplies in conjunction with heater timing, and an audio mute switch in place of the HV standby... but I would also be wary of running power tubes within an inch of their lives too. I just might consider eliminating the standby switch (replacing with a "less conventional" mute switch in these applications and would feel ok about it.