Yeah, polishing is always easy with the proper power polishing tools.
Unfortunately, not everyone has those power tools .
Good point. My friend owns a professional buffer, even that struggles to get deep scratches out. If things get too hot it can also warp or cause blooming in some acrylic lids.
I use 1500 grit wet and dry under a running tap, then 2000 grit. I finish off with jeweller's rouge which I dilute with mineral spirits and apply with a cotton cloth. Fairly easy to get a mirror shine for peanuts, and just as good as expensive polishing compounds. Jeweller's rouge is wax mixed with a polishing compound, I use the red one.
Most important thing is having immaculately clean cloths to do the last polishing, acrylic scratches easily and even tiny particles embedded in the cloth will cause visible marks on highly polished lids.
Those cheap hand orbital polishers don't have enough torque to move acrylic, that is what buffing entails.