The link to the Odyssey page mainly refers to the initial break-in period for the amplifiers. Obviously not everyone will agree with those statements but for everyone who doesnt there just as many who do.

It does take a few hours before the amp is warmed up and stabilized, I leave mine powered on 24/7, one, because the power switch is on the back and not convenient to turn off, and because other than drawing a few extra watts for no good reason i see no point in turning them off.

Haoleb's Audio/DIY Website