I am probably over thinking things...
Several times Jon has thought about how dragons would make the defense of the Wall easier. He and Sam even had a discussion about how Targeryns tried to hatch dragon eggs after the last one died, to no avail. Now that Dany has hatched her eggs, could another person do so? Does the person have to be a Targeryn or if someone has an egg and enough heat could anyone do it?
They say that old spells, etc are regaining potency. Is having the ability to hatch dragons specific to the person like warging? It is a talent that seems to touch a few.
Even if Dany reclaims the throne, she is the only Targeryn left (other than Aemon). Granted she could marry, but if she is barren as the story suggests, the land is bloodied for a one off monarch. Plus, all of her dragons are male. They will not be continuing their bloodline either.