I don't think the slight recess you find on those chips compare to the depth of the recess you would find on a china clay chip without a label like the royals or whatever. How much do you have to mill out of those chips you mention to accept a label? Think about milling a TCH solid then hot stamping inside that milled out area. I stand by my statement that that would not look or feel good. Keep in mind this is my option and I have not done this so take that for what its worth.
It depends on how well used the THC chips are. A typical well-used THC hot stamp where the hot stamp is either mostly worn out or at least feels like it has worn flat has enough of a recess to allow application of a thin, unlaminated label without causing spinners.
But you are generally correct in that the recess would not be as deep as on a new china clay (or a base hybrid ceramic). If anyone is attempting to apply a laminated sticker to a hot stamp clay chip, they must be milled first. It doesn't require a lot of material to be taken out, just enough to cover the thickness of the sticker+laminate, i.e. pretty thin. In my experience, it is easier to mill out a minty condition chip than a well used condition chip (with an undermount router).
I don't know if there's much success out there when attempting to re-stamp a hot stamped chip that has already been milled out. I would be afraid that the weakening of the chip from the material that needs to be milled out on both sides may compromise the integrity of the chip enough to risk breakage during the second stamping process. If it worked, though, I would have no reason to believe that it won't/couldn't look good. Any thoughts,
@AK Chip ?