With the new enable hair growth feature coming to HSY, do you think haircuts are coming soon?

No, I don't think so.

Hair growth for facial/body hair is simpler because you're largely dealing with flat 2D textures that layer over the sim's body, and in the case of beards, a few 3D meshes (many of which are still close to the face).

Head hair has a lot more variety, style and length. There's no easy way (that I can see) to create a system of hair growth on the head that doesn't involve your sim going from "bald headed" straight to "full head of hair" and that would probably look silly to most people.

Plus they have a stylist chair that came in Get Famous. I could see them using that code to add a salon feature that lets your sim have their hair dyed or changed, but not a system where your sim's hair is cut and then grows.