Are there any downsides to interrupting currents between the PSU and a PCB, say using a set of relays, or plain old switches? I mean the 5V and 12V lines. Does it make any difference to the game? I'm an electronics noob so...
Hard to say as it depends upon the quality of your supply. I the load on some of the voltage rails suddenly drops to zero (by disconnecting a game board), the voltage could jump up a little for a fraction of a second. If you connect another gameboard, it might get a higher voltage than it expects. So basically, the correct procedure guranteed to work without issues would be switch supply off, wait a couple of seconds, switch gameboards with a relais or mosfet or something similar and turn on the supply again. A good power supply should be able to soft start under load and reach it's expected output voltage pretty fast without overshoot.
Well I wasn't thinking about switching between multiple boards, but rather things like having the option to control on/off/reset via a microcontroller + relay. I only (dis)connect game boards with all power off.
Anyway, thank you!