Plenty of cities have traffic light preemption for buses. Portland does it for the MAX (not a bus, I know), and Chicago tried it when I lived there, etc. (The problem then becomes, what happens when an emergency vehicle AND a bus both preempt the traffic light? In Portland anyway, MAX wins. That doesn't always mean the emergency vehicle stops, though, with predictable results.)
I rode the bus route daily when they tried it in Chicago and it didn't speed things up much. One at a time, slowly, slowly, people climbed on board, paid their fare, couldn't move into the bus because it was crowded, and then the next person in line blocked the doors until someone moved enough for them to get on... five minutes, the bus was on its way through a fresh green traffic signal. Great.
(Continuing the rant, what about paying the fare off the bus? I've tried this in NYC, and every time I've used SBS, fare collectors have stopped the bus, slowly checked everyone's tickets with the bus stopped, and then gotten off. Waiting at a red light or two is nothing compared to that. I'm sure by the time you include the fare inspectors' salaries, some supervisors to fire them when they do the collection with the bus stopped, and recruiters for new fare inspectors... it's a mega money losing operation. But oh no, we could never make it free, only Communists would want free bus service!)