Prioritization works when the traffic otherwise is light enough to be moving. Sacramento prioritizes light rail at most downtown signals, for instance, but it doesn't help when the cross street is all backed up and the people sitting on the tracks trying to make a turn can't move. It's often quicker, if going to a place near the county buildings or library, to get off at 7th/K and walk a couple of extra blocks in the late afternoon, due to the 7th & I intersection blocking that way and preventing the train from getting to the next station at 7th & H. The prioritization for that signal can hold it only so long.

Ages ago, a semi-express bus I rode sometimes in Santa Cruz (on days when I didn't want to drive or bike) could preempt the signal at Soquel/Water/Morrissey using the standard (at the time) flasher gadget also used by emergency vehicles. It helped in the late afternoon when that (5-way) intersection would get massively clogged. Since then, the intersection has been redesigned and works slightly better. That intersection also has "pedestrian buttons" at the curb for bicyclists to use; very helpful, and were present in the late 1970s (I could get to work faster on a bike than driving).