When your amp is on standby, the only thing that is really "on" is the heaters for the tubes. You could hot-swap tubes, but there are a few problems.
1. Pulling one tube decreases the draw on the heater, so the other filaments receive higher voltage than they should.
2. Tubes are generally pretty hot after the filaments have been powered up for a while. This is bad for your fingers.
3. The new tubes need to be warmed up anyway.
You shouldn't really have to wait on the caps to drain to change tubes (just like you can change a light bulb with the light turned on). Just shut off the amp. Let the tubes cool to the touch. Change the tubes. Turn the amp onto Standby. Let the new tubes warm up. See how it sounds.
The only things in the amp that need warming up are the tubes. Capacitors reach charge within seconds of having power applied, resisters always resist, and transformers always transform.