That's such a funny problem nowadays. It even happens with x/pro since most of the times the cutscenes are only 1080p.It's not something I've noticed as much.
I think Final Fantasy X cleaned up their cutscenes. And Jak and Daxter actually had their cutscenes running in real time. Which is something I've never seen anyone talk about.
But their cutscenes looked pretty clean. (At least what I remember of them. I might be mistaken.)