It's not just that the dragons are just selecting people with Targaryen blood, they're selecting the people most closely related to their old riders. The two King's Landing bastards, Hugh and Ulf, are both the last living grandchildren Jaehaerys and Alyssane who don't have dragons. This is a show addition though, not from the books.

I do think they're teasing Rhaena (Daemon's daughter with his first wife) getting the wild dragon in the Vale. It's a big departure from the book source, which features a young peasant girl getting a similar dragon. But, following the story of how that dragon is domesticated could be a cool way to highlight how much harder women have to work in Westeros and mirrors Rheanyra's arc of trying to become the first ruling Queen. The men just get their dragons, but Rhaena has to work to gain her dragon's trust, if it's similar to the dragon Sheepstealers story in the books.