From what I've learned from the guys at the Cold War Air Museum, the biggest problem with the Soviet fighters is the endurance and runway needs. Too little endurance, and too much runway. And when I say "too much runway" I mean that they have to operate from a runway with at least 6,000 feet, peferably 8,000 feet, and being experimental, that means they can't get to a lot of those runways due to the rules about where you can operate them from without a lot of written clearances (in the US at least). I think if there were sufficient runways at non-restricted airports and the demand for them on the airshow circuit was a bit higher, you'd see more of them, but until then, the expense and restrictions on operation make them somewhat impractical for most to operate.
As for the maintenance issue, you're right that most everything was designed to be repaired or serviced at depot level, but the difficulty of servicing them at depot is no more than any other airplane. The idea with the Soviet aircraft was that you build everything so tough that each depot visit, you simply replace them and let the shop inspect and/or overhaul the part independent of the airplane. The trainers are built on the same maintenance philosophy as the fighters, so that's not why the trainers are more prevalent. It's simply that they're built with more endurance, are easier on fuel consumption, and have fewer "gotchas" than the fighters, making them much more economical to operate. Plus, they can all carry at least one passenger so you can share the fun.