It's been tried - with mixed success.
I've done it a few times - used paulsons who's hotstamp was removed by a milling machine.
First, the inlay has to be milled perfectly flat and uniformly. The new recess has to be 100% perfectly parallel with the face of the chip.
Second, you can't move any more material than what the original hotstamp would require. This also helps getting the die deep enough in the recess to create an impression on the 2nd hotstamp.
Third, the hotstamed area will be made harder by the heating/cooling process of the previous stamp, so hotstamping it again generally leads to only partially successful results, so the smaller the die used most likely the better.
That being said - a member here a few years ago was a machinist and managed to mill a hundred or so. I hotstamped them with a really simple die afterwards. It was good enough for him, but no where near perfect.