>A monorail suspended over the roadway would offer better stability
Building elevated rail infrastructure is very expensive though. The material required to build infrastructure supporting a "tall bus" is substantially less. Furthermore, the bus doesn't contribute to visual pollution quite as much.
It might be slower than a train, but it's certainly faster than a normal bus. There are a few places I think this idea would be extremely helpful in Chicago. Our road system is a very regular grid, with major streets every 8 blocks, and semi-major streets every 4, both of which are signaled. Bus stops are usually at these intersections. These intersections are also the places where people are most likely to want to turn.
If you banned left turns outside of signaled intersections on these bus routes, and the bus stopped on the near side of every intersection, you wouldn't run the risk of the bus overtaking cars and hitting them. Instead, the bus would get a signal to move first, and cars could proceed afterwards.
Some of the slowest buses in Chicago are on routes that aren't served by trains. Trains only go to and from the central business district, and so you need to either take a bus or drive to go anywhere else. The immense volume of car traffic also slows down the buses, some of which are barely faster than walking speed. I used to live 4 miles from my job, but taking a bus would have taken over an hour. That is the time with a single transfer, 10 minute headways, and a bus stop in front of my apartment and a bus stop in front of my office.