IMO, there's no categorical correlation between abrasive/chemical polishes and machine/hand application.
Mechanical/abrasive polishes can work just fine by hand as long as the abrasives break down (and most products that work by PC also work fine by hand); it's when you run into rotary-only abrasive products that you have to be careful.
And note that often, products that contain "abrasive ingredients" are functionally nonabrasive on auto paint anyhow; the "abrasives" just make them easier to use, *especially* by hand.