Secondly you avoid any possible damage should the piece of gear electrically fail while you're not there......

An actual example a studio in my area that left all their equipment
On all the time.... there was a failure in his 2 inch tape recorder's
Motor Drive Amp and the machine went into full torque on the supply motor.
And alas it had a Master 2 inch tape loaded up.    It ran that way
for 3 days until the owner came in to do the next session   '!!!!
Each turn of the reel - once the tape came to the end - broke off an fraction
of an inch of tape so when the engineer/owner returned to his studio over
half the reel of tape was in small pieces on the floor....
all because he left the machine ON and a transistor failed.

I've seen very poorly designed power amps put out DC directly to
speakers, power supplys can fail putting out huge voltages and burn up
ICs and whole cards....and so on, so it's just safer if you turn all the
equipment Off when you're gonna leave for the day or for a few days...

Of course if you're just leaving for a few of hours, I'd leave it On......

The idea of leaving gear turned ON all the time comes from the days of
the all tube equipment studio (back before the late 60's).
 
For tubes you've got to let them warm up and reach their
normal operating temperature, and even then you'd have to wait until it
quieted down.   Rather than wait an hour for all this to happen (and the
corresponding movement of the tube's filament during turn-on and
turn-off) the gear was left ON all the time in busy studios.
But this was in studios with nothing but tube gear, so you might
have had 30 or 40 pieces of tube equipment to heat up before each
session....     Now days you might have a couple pieces of tube
gear in your studio, and yes you need to turn these ON a good hour
before you use them, but don't leave them ON all the time   !!

Todays non-tube gear doesn't need warming up at all - of course you should be
running tape on your analog tape recorders as you're tidying up the studio
and before you start to align the machine.... say running 10 minutes of
tape should do it in the morning if the machine's been Off overnight...

And Yes there is some very minor stress on the Power Supplies, but it's really
minor in a well built unit and should be of no concern.

Of course you'll want to have a shut-down procedure so there aren't
huge pops in the monitors as you turn it all off and back on....

Another reason to turn the gear OFF is that all equipment creates heat internally...
and this will dry out caps and greatly shorten their life-time.

SO TURN YOUR EQUIPMENT OFF when you leave for the night or a day or two   !!!