Should it be necessary to have a PS2, PS3 AND PS4 hooked up all at once to play?

[Mmmfishtacos]

I had a BC ps3, I played 3 PS2 games on it for a total of 5 hours, Maybe. I never once put a ps1 disk in the system. BC isn't a selling point for a new system with new games. Key word new. My PS3 will be moved into the bed room along with my Samsung 720p Plasma. PS4 and a brand new 1080p tv will go in the living room.