I have a bunch of different old consoles and vintage computers (not "444" of course) and used to try to have them all hooked up, it was such a miserable rats nest of wires. I eventually settled on just using one at a time (I am only human, after all).

Whatever I'm playing gets the prime hookup spot in front of the TV, everything else gets stored neatly on a shelf or in a box. Cables and controllers are in individually labelled zipper storage bags, in bin drawers, out of sight until they are needed...

Of course, hooking them all up is a hobby itself... It's easy to go down a rabbit hole of scalers and SCART switches and RGB mods and then you suddenly find yourself a couple thousand dollars poorer.