Generally you can have bearings that are small/fast/precise or cheap - generally not all 4.
But the heads are mostly kept above the surface by aerodynamic effects - effectively they are held in a thin air film which stops them touching the platter.
It still needs a radial bearing to attach it to the motor - especially if you aren't mounting this perfectly flat and level. It can use an air cushion effect to reduce the planarity demands of the bearing to keep the heat transfer surfaces parallel - but this is very different to 'floating' a 10mg sprung drive head