When using a power conditioner, why is it advised to run amps directly to the wall?

Power Conditioners do not solve any of these common problems:

See PDF here read pages 11 12 13 38

Mike

Otherwise, straight to the wall so you don't limit current...this is according to Nelson Pass, who also recommends using the power cord that comes with his amps.

Nelson who? What? Who dat? What kinda name is Nelson anyways? You gonna trust a dude called Nelson? No my man lemme tell you where it's at. I know a lot of dudes on the internet, and they do lotsa research from their barca-loungers, know what I mean? And they say you don't want no cheap cables, you want $5000 cables made of solid stainless steel. And if you can't swing $5000 cables well that sucks for ya but don't try and tell us your pathetic desinformation cause we know the truth! Look at that Nelson guy who can't even buy himself a cable. What does he know? Huh? I know who I believe, man. I do my research too.

By extension, is the common wisdom NOT to plug a powered subwoofer into a power conditioner? I’ll try it both ways.

If your system is transparent and resolving, you will hear the power conditioner.

There are active (Puritan, Audioquest) and passive (Shunyata) power conditioners. Then you have power regenerators (PS Audio) and isolation transformers (i.e. Torus). 
 

Good passive power conditioners like the older Shunyata Hydra, which I have used for many years with several amps including Pass Labs X250.5 did not negatively impacted the performance of the system. Then I made a mistake of replacing the Shunyata with Puritan PSM156. Not only did it limit the current to the amplifier (Pass XA30.8) but it also resulted in negatively impacting preamp and DAC. Yes it sounds like it gives quieter background but all that is is excessive filtering and limiting of dynamics. I ended up running all my components directly from the audiophile grade outlets that DO make a difference and sold the Puritan. 
For those who want to ask me if I measured the effect or conducted some sort of blind testing, I did not and didn’t need to. I heard it all. Plus when I plugged my Pass X260.8 mono amps into the Puritan it started ringing like your grandmother’s rotary phone. No need to measure the effect. That thing is pure and utter garbage. 
 

If I ever go back to using a power conditioner it will be a passive unit and only for source components. Properly designed amplifiers with good power supplies don’t need power conditioning. Just isolate your digital from the amp using two dedicated circuits and you are good to go. If in apartment I’d just rely on passive power conditioning.