I did. Pay attention.
(Just kidding--I'm feeling like a smartass today).
Sure. I still wouldn't do it that way unless I couldn't use an IR-equipped player (which could well be the case here). You can make the IR repeater using just an IR transmitter/receiver pair and a line driver. You could put those into an XLR housing and use the cable snake to route to backstage (you could do this with your idea too, of course). There are no requirements of the player unit other than that it has an IR remote--it wouldn't even require actual push switches for functionality. And while I agree 2 solenoids isn't much in the way of moving parts, the IR repeater has 0 moving parts--and no mechanical setup is needed to mate solenoids to buttons on the unit: you just aim the repeater head at the IR receiver on the unit.
All in all I don't think either method has a huge advantage over the other in terms of cost or complexity: both are simple and easy to make. I'd rather go with the fully electronic one for the reasons stated, but if the unit doesn't have IR remote control and you can't use one that does, then there's nothing wrong with the solenoid idea. If the IR remote control option is there, however, I'd prefer to go with that.
Actually in a pro stage environment what I'd really want would be a proper stage CD player with MIDI Show Control or similar.
But that's a whole different wave in a whole different ocean.
Cheers,
Torben