Eventually, the interstellar pest control firm will come by.
Back to the point, I'll suggest that the Novick dragons are so well integrated across their world that they would survive and maybe prosper in some. The Asian, South American, North American Dragons and African dragons seemed to fit. The British ones seem to on the verge of a dragons rights movement. The Eastern European dragons are enslaved. One can imagine if they learn of the roles in other countries, we can see defections.
A GOT dragon today, might land in some zoo. Hard to catch but might be bred for captivity. They would have no utility, except for some obscure uses, such as elephants are used in chores in places where machinery has a hard time.
We certainly don't need a Valheru on one of their dragons around here. That combo can planet smash.