Given the inherent randomness of traffic, it might just make more rational sense to have busses at 'intervals' instead of specific times.

Might make for more throughput.

Handling that is an infrastructure and priority question. Given the political will one can build bus lanes and equip buses with a radio system which enables priority on traffic lights. In my hometown (Munich, Germany) this works quite well and most buses see mostly green lights.

There was a discussion on reddit recently talking about this issue in context of LA's buses. People don't mind if the bus is on time if there's one every 5-10 minutes but in non-rush hour times, having to wait 20+ min at a stop is too long.

In normal situations, the arrival time doesn't change, and the train pulls in within seconds of the right time. It is startlingly precise (to someone used to American transit), even during high traffic times in the middle of Tokyo.

Off the top of my head, during busy hours for me going towards Tokyo there would be a train every 5-8 minutes. (And there are multiple lines, although I'm quite far out, so they condense as they get closer).

Yes, only Houston has this problem, not almost every single bus system in the world.

Aghh, I hate the Minneapolis bus system, I remember two times in the winter when the bus just didn't come, real nice when it's -8F outside. Or buses being 15 minutes late. But worse of all are the bus drivers themselves. However the Blue Line and Green Line follow the schedule much better then the buses. If your in Minneapolis your best off either driving, biking, taking LRT or catching a Lyft or Uber.