Surely the groove depth changes with signal? A right channel signal for example must cut into and out of the lacquer at 45 degrees. I can see that a heated cutting stylus will help the process, but then does that affect the final profile as the material cools?
I used to hear about this thing called rebound associated with lacquers but yet to experience it. Yes, the groove wall is cut at a 45 degree angle, so if you were to cut an out-of-phase bass signal, the groove would indeed modulate up and down. Of course, the needle would not be able to track it, and such a signal fortunately does not exist in nature. If we encounter studio productions where out-of-phase information is a problem, we have a simple passive processor that takes care of it. So groove depth can be considered a constant.
Another way to look at this is if the cartridge body rises higher, that is a change in groove depth, if the needle simply traces a signal, the groove depth has not changed.