99% of people just want a car that looks clean and shiny. Not all polishes break down, but without going down the machine polishing rabbit hole, I started out using t-cut by hand on two cars - fantastic results. You won’t see it mentioned on enthusiast forums, but the fact that it is still available shows that it has a place in the market.
If you just want to remove ingrained dirt then Mitchell & King ‘Pure’ polish will give fantastic results by hand.
Pure doesn’t contain any abrasives, t-cut was originally a go to product to remove oxidation.