The fact that the 20mph limit didn't slow schedules down is the biggest red flag that stops are too close together and poorly sited. I hate saying London has it better, but even Glasgow does stop spacing better.
A lot of 20 mph limits have been applied to streets where it would be hard to go faster anyway - many of the 'main' roads are still 30.
Edinburgh's problems are narrow roads for modern vehicles, too much on-street parking, lots of traffic signals, a lack of routes avoiding the city centre, little bus priority poorly enforced, etc. No doubt there are cases where stops could be improved, but to see it as a major solution is wrong, and the down side for some passengers is obvious.