They never re use mine. I have wondered the same thing. At least I make them give me the crown. I have 3 or 4 by now that I could melt down and make into something. But,I think they are only 10k gold,which is the lowest alloy that can ce called gold. Also known as "New York gold".
'Dental' gold alloy, was traditionally 22K. Yellow version anyway. "White" gold MUST have more of other elements. Payback is that it is harder, stronger, not quite as obvious if a person has to open his mouth frequently. As with Silver-Mercury amalgam, white gold is also something of a Biocide. Yellow Gold doesn't interfere with microbes. Cuts both ways, that attribute set - reduced decay, halitosis, vs possible allergies, long-term heavy-metal effects. Humans are Biological critters, just as Microbes are.
Used to be the pennyweight of removed Gold was an offset to the cost of new gold used. It isn't usually all that much compared to the Dentist's skilled labor. Dentist is also in a better position to have it recycled than Joe Average ordinarily is anyway.
The 'primary' re-refiners - those with the highest percentage of recovery and payback, even paying on trace metals - do not want stray sources of materials, only traceable, reputable, and established ones.
Helps keep their slender margins from being consumed if found to be processing stolen metals.
That said, about once a year, someone brought in salvaged dental gold into our firm to be crafted into a pendant and set with diamonds or such. Sometimes recovered from a deceased spouse. At 22K, it was actually a bit too soft to easily insure retention of the gemstone. Needed more metal, shrouded the stone more than our usual 18K or 14K.
Y'know humans? Strange folk some days.