Do all reptiles have the capacity to grow feathers, like dinosaurs?

I think the idea of feathers being an inherently reptilian trait would sort of change my (bad) opinion on feathered dinosaurs for the better. This is because the big reason I like dinosaurs is them being reptilian, but feathers kind of took away from that for me, but if feathers are truly a reptilian trait as well as avian, that might shift my view.