A good GM is trying to make things more fun, and if too many things are left to chance, it wouldn't be as epic. So there's no internal conflict in doing both GM and PCs, because ultimately the goal is tell an epic adventure. But I agree that sometimes you need to make an impartial decision. And nothings easier then /r D20 vs a number in your head. Love it!
As much fun as I'm having in single player, I'd also love to try being a GM while also controlling a PC in the party with other people. The scenario could be where the heroes fight a boss who upon defeat gives his word to help the party. The players must then take everything that player says with suspicion (both because he's controlled by the GM and because he was an old foe). The best part is that instead of just being an NPC, you actually use a real character sheet, maybe even one of your old characters with a neutral or evil alignment. Then you can level him with the party, and have all the fun and satisfaction of controlling a PC while also directing the adventure as GM.
Not sure if that's often done. But it looks like Roll20 is built to support one person playing both GM and a PC in a live game.
Reading the posts on LFG forums, it sounds like alot of GMs really miss the experience of being a player. I think they long for the tactical depth of combat as a player, which is much much richer than the limited powers of monsters (even solos don't have enough powers to satisfy me), so this could make GM'ing even more fun.