There is an Engine that works on Vita and not the Xone or Switch?
I bet there are. Without proper tools, an engine will not work on a new system. It's not like Sony could release a PS5 today and Unreal Engine 4 would magically work with it. Atlus did not make a single game for Switch and Xbox One so far, so it's entirely possible their engine that was used in Catherine, Persona 5 and Persona DAN is not fully fuctional on these systems.
Wasn't the Engine originally working on 360?
First of all Xbox One and Xbox 360 are not the same system. Furthermore, the last X360 game developed internally at Atlus was OG Catherine in 2011. I'm sure there were enhancements, improvements and changes to the engine that make it a very different tool.
Aren't PS3 and PS4 architecture wildly different?
That's irrelevant in this case considering both systems had a game running on internal Atlus engine (Persona 5).
I think if ATLUS wanted to do this they would.
No one said the game is never coming to other systems.
Note that all I do is assume. I have no knowledge in Atlus' internal processes and game development whatsoever. What I'm sure of is that assuming some sort of technical difficulties makes more sense than "a company hates money" point of view. I would even take the argument that Sony bought the exclusivity for the game, but honestly that makes no sense considering a Vita version is in the works and we all know Sony forgot what Vita is.