It’s a fun thought experiment! Napkin maths assuming max 78RPM at 300mm, min 33RPM at 80mm (I think inner groove is bigger than this but wateva) gives ~3 to ~30 microns for half-wavelength of 20kHz (not that 20k is really stamped into vinyl). Actually, not bad.

Amplitude though, 78s are the best case scenario, and assuming mono for simplicity, they have lateral displacement of about 76 microns peak to peak. So assuming 1 micron resolution that’s just over 6 bits of dynamic range absolute best case. Crunchy.

Dodgy maths aside there are lots of reasons this would not produce a good sound. There are maybe clever things you could do with a spinning bed or something? but even then.

At that point though even a normal analogue cutter head will be easier!

See lathetrolls.com if this particular kind of masochism interests you.