Domain Level Games
I think you have two really good points there, TK. Provided you catch it early enough, you can perhaps do something to prevent PC breakaway (though if your intervention is obvious, you could lose the player).
However, there is no real way around GM burnout apart from finding (or devising) a set of rules that allows players (and GMs) to manage domain games realistically with minimal effort. If anyone finds such a rule set, please let me know!
The problem, of course, is that running a nation is complex, and any ruleset that represents it with any veracity is also going to be complex. And, as you say, the GM has to run every nation on the map.
Because of the complexity, and the typical length of domain campaigns, you also need to find some very special players - people who are prepared to spend years in a single game, people who are comfortable with mathematics, people for whom managing their own domain is more important than painting the map, for whom playing is more important than winning.
There is usually far too much effort involved, for players and GM. There are easier ways to get your gaming kicks. That is what you need to overcome to make a domain game work.
Unfortunately, it's like saying all you need to explore the universe is a decent faster-than-light drive. The solution is obvious. Creating that solution is pretty much impossible. :(