I agree with Lonman for several reasons. Speakers are not designed to have DC running through them and the distortion is DC when an amp is red lined. It's much better to have twice the amp or more than the speakers and control yourself by not running the amp too high. This is also good for the amp as they are better able to handle the heat they generate at half power versus red lined. I also think that speakers, on the other hand, operate best when pushed to their program rating or slightly higher with a good clean signal. The cabs are designed to resonate best at certain amplitudes.
Gain staging is also important to the speaker. Distorting at the preamp, for instance, simply provides a DC signal to amplify all the way through the chain.
I don't bite on the breaking in and warming up of the speakers. If a speaker has an issue when its cold or first put into use, it has an issue period. You might be able to warm up a speaker with an issue and maybe get less coil sticking, but the speaker still has an issue and should be replaced.
Turning the amp down and input signals down when powering up/down eliminates the initial DC signal most amps provide hence the pop. After that, the speakers should be ready to go. I have an old STX1600 amp I use at home that I love and I think it has a delay circuit to eliminate that initial POP sent to speakers at power up and power down, although I am not gonna test it..
Oops, see others have covered this as well.. sorry about that!..