[dreem]

Even currently, many world class high-precision mirrors are ground and polished by hand. I believe the machines you're describing are just copying the same procedure that is done by hand (a robot or swivel arm imitates the motion that a hand would make), and this process produces surfaces that have an average roughness of less than 1 Angstrom across the optic.

However, there have been other technologies that will polish out tiny non-uniformities and 'bumps' on the order of nanometers tall across a few square microns. These technologies, such as MRF finishing https://qedmrf.com/en/mrfpolishing/mrf-technology/how-it-wor... are the current state of the art to get the best surface finish.