> Making these extra stops causes the bus to 'miss' the light cycle at almost every stop.

This would be a much bigger change, but it's also possible for the lights to give priority to buses. When a bus approaches a light, that should trigger the lights to advance to the part of the cycle that gives the bus the green light. That way, you prioritize the 20 people in the bus rather than the 10 people each in their own car.

This happens with trams in the German city I live in. The other advantage is energy efficiency, apparently - if you can keep them traveling at a consistent speed, then they can maintain momentum, as opposed to if they're constantly stopping and starting and need to spend more energy getting up to speed.

It's slightly irritating as a pedestrian when you're waiting to cross the road to get to a tram stop, and you see that the tram is coming in less than a minute, and you know you're not going to be able to cross in time. But that's the sort of slight irritation I'm okay with for better fuel efficiency and faster trams.