"Forced to play as a trooper"? Like, what were you even expecting? That's the core gameplay.
But there is no real answer for this, too many variables are involved. For me, it's mostly like 6-7 minutes, but I don't really keep count, it's better to plan your hero spawn rather than rush in as soon as you have the points. I rarely spawn as a hero in the first phase of Theed and Kashyyyk, it's just too open. Heroes regenerate some health, but in exchange, they are really vulnerable compared to the 2015 Battlefront game.
Also, sometimes (as mentioned before) the defending team is so good the match ends in the first phase - that mostly results in little to none hero play, there simply isn't enough time. It takes a little time to find your playstyle, and that might discourage you as a beginner player, but despite what many say, this is more of a casual experience, and you pick up the pace fairly easily.
But I wouldn't stress about this, there has never been a match for me (excluding these prematurely ending ones) where I couldn't play as a hero. Yes, sometimes they snatch them right before you, but I've never experienced something like 2 guys being alive the whole game as heroes from the start. Also, in the final phase, hero count goes up to 4 from 2, so more people get to try them.
Edit: my experiences are on Xbox One, I don't know how it might differ on PC.
If you are able to score 6,000 BP in 6-7 minutes then you are having one extremely good match.
I'd say that on average a top player gets about 600 BP per minute. Again, this is BP, not score.
So 10-13 minutes I feel is average for a top player to get into a hero. That said, I tend to save my BP and get heroes at certain stages or points in stages that I feel they are the most effective. So just because you have enough BP for a hero doesn't mean you necessarily should buy a hero. There are certain stages and maps where infantry are very vulnerable and it's fairly likely you'll just be wasting your BP. For instance, heroes aren't great on the first stage of Hoth because they are easily focused fired in the wide open (or run over with a tauntaun). The same is true for the first stage of star killer except it is speeders rather than tauntauns.
As far as heroes being alive the whole match... well I rarely die with either Rey or Bossk. If I do, it's usually as a desperate final move to try to take victory from the jaws of defeat. You just don't notice a player being a hero all game often because the limit on the amount of heroes available goes up with each stage. By the final stage there are typically 4 heroes allowed per team and the tactics get more desperate so generally most players with enough BP get a turn on one of the lesser heroes at least..
