Yeah, I had the same idea a few years ago and created blueprints for two versions. I ended up never going beyond an early blueprint stage.
One was a version where rotating the monitor involved opening the back and, using a heavy duty VESA mount I located, rotate and reposition the monitor (I discovered the same problem BadMouth mentioned). I didn't really desire front access to the monitor because I didn't want anyone else gaining access to the inside of the cab and I was really interested in doing a really nice "face" which would have precluded opening the front anyways. At the time, none of my cabs were backed against the wall so accessing it from behind wouldn't have been that big a deal anyways.
The second design dropped the entire manual process and involved a set of motors (I'm using the term motors inclusive. That means including servos and steppers for those who can't figure it out.) and actuators all driven by a custom controller. I even worked out the geometry and drew up a set of blueprints, circuit schematics, and tested the process via animation showing two different rotation paths. Never got around to writing some test software. I still have most, if not all, of the files archived away somewhere, if my house wasn't so trashed (remodel) I might actually know where they are.

In the end, I decided that the effort of the former and the cost of the latter ultimately could not justify the "coolness" factor of that kind of rotating monitor. In short, I felt it would work if one went cheap but had to contend with those particular issues, or went for broke in which case the money could be better used towards better "features" anyways. Any option "in between" would have resulted in a "classic" configuration which is something I didn't want.
It is unquestionably "doable", DMWorking247's bartop and some of the really awesome rotating monitor cabinets attests to that. It just wasn't the cabinet for me. Here is another example of a really great rotating cabinet where instead of trying to fit a round peg into a square hole just make the hole round;
Retro-Futuristic Mame cabinet.