It's difficult to get power amp distortion without over-driving it with the preamp. When you crank the master, all you're doing is opening the door between the preamp and power amp. If nothing's coming in, nothing happens. And of course, all points in between. So, you can crank your master to 11, but if the preamp is at 1, it's gonna be pretty clean. Probably as clean as it can get.
Power amp distortion is largely over-hyped. It's difficult to get unless you really crank everything. At that point, with a tube amp, you get some odd-order harmonic distortion at some point, which continues until you get into clipping distortion. That's sometimes desirable in tube amps, depending on the sound you want. In solid state amps, you never want clipping distortion - it's awful. It's why many of the older SS amps have such a bad reputation. Even-order harmonics and hard clipping. To call it "harsh" is an understatement. It's an ice pick in the ear.
A lot of what's called power amp distortion is actually power supply sag. There's an inverse relationship between voltage and current in a constricted circuit, so if you try to draw more current than is available, the voltage drops. That changes how the tube behaves. It's not linear any more. This is also frequency dependant, as lower frequencies require more power than higher ones do (more area under the curve). All that variation is why it has traditionally been somewhere between difficult and impossible to model tubes with solid state devices, which are highly linear. The natural compression that occurs with tubes is almost infinitely variable. It's also delicious, sonically, which is why tube amps are still popular. These days, there are tricks you can do with solid state stuff, but it requires a lot of expensive processing power.
It's a balancing act.
In any event, as long as you stay withing design parameters, none of it "hurts" the amp. It just changes the way it sounds. Sometimes you want it louder or softer, sometimes you want it more or less distorted. If anything gets hurt, it's usually the speakers. They can only dissipate so much heat, and if you exceed that, you'll either warp or open the voice coils. Either way, it's trashed.