Turntable power supply/motor’s role in SQ for belt drive TT

I’m trying to understand the ways that an upgraded motor/power supply can improve the sound quality of a belt driven turntable. 

OK - speed control that is more precise, I get that. But is there some inherent electrical noise from the motor that makes it way into the analog signal thus producing an audible distortion through the cartridge/phono stage?

I’m also curious about why an AC motor would be less desirable than a DC motor (for a belt driven turntable. 

Some back story: I am preparing to send my 35 year old Linn Sondek LP12 turntable out for servicing and upgrades. Linn has the promotion going on where you get the new Karousel bearing for “free” when you spend at least $4,000 USD. Kind of a gimmick, I know. But I would like to get at least the Lingo 4 power supply and am considering “Akurate” level “Radikal” power supply for more $$. I am looking forward to spinning my old vinyl again soon and hopefully with upgraded SQ as well. 

Thanks for any replies.