You're insane
Keep your systems then and put them behind glass in your living room. Use an emulator for your cabinet. Do you remember having to open up an arcade cabinet to switch games in the arcade? What about ruining that nastolgia? With an emulator and front end you can fire up whichever system you want and select between hundreds of games all on-screen. Not to mention the many, perhaps dozens of hours you will save by not figuring out and implementing a wiring solution for all those systems. Just think of all the times you are going to bump your head while bent over inside your cabinet blowing in your NES cartridges and using the reset trick in an attempt to get them to work.
If you continue down this path you'd better hope that you are allowed to bring large personal items into the mental hospital because somebody is going to have to have you commited.
Well console games are meant to be played on a CONSOLE not on an arcade cabinet. So there is 0 nostalga involved as you are playing arcade ports at best. Also acrade controls are not well suited for console games. You could get away with it on the nes, but that's about it.
Also console emulation sucks, to put it blunty. Really old systems like the 2600 and nes emulate well but anything newer is still very much incomplete. The snes's fx chip has still yet to emulated and just forget about the psone. It has about a 50/50 success rate.
In addition, the average arcade game lasts about 5-25 min at the most. The average console game can last hours. What difference does that make? Well when you normally play a console game you are relaxing in a chair or on a couch sitting several feet from the tv, with your arms comfortably in your lap, only moving your thumbs. Now you going to take that same several hours standing up (or in an uncomfortable stool) with your arms at your waist, only about a foot from the monitor, moving both hands in much broader a fashion.
In other words, it will get real old real fast.
Also don't forget that virtually every arcade game on the psx is now emulated.
Wiring wouldn't be much of an issue, but imo it's just a bad idea to start off with.