I've had RAMPS go up in same fashion, screen flicker and smoke. Result was a blown 5V regulator on Arduino Mega, board still works when using USB. The reason for that was me connecting endstop switch between + and - on RAMPS by mistake and homing the printer -> short circuit. One reason to hate RAMPS, it's too easy to make that kind of mistakes since there's no safety features builtin... well it's cheap so what can you expect.

ATX PSUs aren't a bad choice for 3D Printer, I have 2 of my printers running on ATX PSUs without problems. One of those even has the 5VSB and soft on/off implemented so the board itself runs from the PSU's 5V standby and 12V output can be controlled with gcode commands/Duet web UI. Been planning on implementing that to the other ATX powered printer so I could power Raspi and RAMPS from 5VSB and control 12V from Octoprint. It's also an safety feature because that would give me the ability to turn off my printers remotely if something goes wrong.

Not sure about the idea to connect multiple printers to one PSU, in theory it should work as long as the power has enough juice to power both printers, but then again I'm not an electrical engineer so cannot say for sure.