Is there any reason why channel switching is done by relay? Since relay, in the end, is still mechanical (somewhat), is it okay to use physical switch to switch in an out a tube gain stage?

Also, woudl you call "switching resistor and capacitor value" channel switching? because that's basically what Blues Deluxe and Blues Deville does for their "channel"
Ibanez SA-120 (ed.2006)
BluesJr 1996-B + cathode follower + texas Heat
Crate CPB150
Homemade 4 x 10 cab Bass closeback
Metal Muff
They use a relay many times as its easier than running the signal all the way out to the the footswitch in the pedal then back to the amp.