I disagree with this sort of system. 

As one point, it allows for people who do not offer any benefit to their team to manage to play a position of high authority on their team.  Only people who truly earn a position of power should have the power to go with it. 

I also disagree with the slow health loss, it really defeats the purpose of a hero.  The major thing is that heroes were very unbalanced in Battlefront 2, which was why the time limit was put on.  If Heroes were balanced, to the point where how much time you put in to practicing and your outcome in skill would determine your skill (ie, a horrible Hero would almost constantly fail, whereas an excellent Hero would be nearly unbeatable in 1 vs 1 combat of any type), then there would be no need for the gradual loss of health.

However, on your point of the Heroes on each map, I believe that the Commanders of each team could receive one of the Heroes for that team, and the squad leaders get lesser heroes to play with.

So, as an example, on the Death Star Trench Run, the Commander of one team would be Luke Skywalker, and the Commander of the opposing team Darth Vader.  Squad leaders for the Rebels would be "Red Group," with possibly an improved ship or something of the sort, whereas the Imperials would have the elite Vader Guards, also possibly with improved ships.

These are very bad examples, but I really am having difficulty thinking of a good example in the GCW   Hopefully you understand my point from my example.