I think the amps-left-on thing is partly a holdover from vacuum-tube days of early studio work (before the invention of the transistor), when it made sense to leave them on because it takes tube electronics a while to heat up and stabilize.
Now, it only makes sense in professional studio applications where the solid-state gear will be used more or less constantly all day (and night), to reduce all those turn-on transients that would otherwise occur.
Alan
Agreed on the tube and pro comments, but I think the "Ultra High Fidelity" folks believe it also impacts sound quality in solid state gear - see what I did there incorporating a magazine that falls into that group?!?!
