On the Viva BRTs I noticed that left turning cars are prioritized over transit vehicles. Can anyone explain why? To me, it would make more sense to allow cars to turn left after the transit vehicle has passed.
Left turning cars are not prioritized above streetcars/buses per se, it's just that transit vehicles are not prioritized over left turning cars (which is indeed an issue given the aforementioned occupancy difference).
Simply changing the order of the phases from leading (before through traffic) to lagging (after through traffic) would make absolutely no difference to transit delays. It's exactly the same green time, simply at a different point in the cycle. As Tuscani01 mentioned, Spadina and Lakeshore currently operates with a lagging left turn phase, meaning that left turns go after streetcars. And that in itself does nothing to reduce the astronomical delays faced by streetcars at that intersection.
There are two primary methods to prioritize transit vehicles over left turns: phase insertion and phase rotation.
Phase insertion is where an extra phase is added in the cycle to provide a green to transit. So with leading left turns (as on St. Clair, Viva Rapidways, most of Spadina) if there's a streetcar waiting or approaching at the point where the left turn phase would normally start, it would run an additional east-west phase first, then go back to the regular sequence (left turns, then east-west again). The main question in this option is which movements should be permitted during the inserted phase. If only transit is permitted it can be very short, with as little as 6 seconds of green (around 12 seconds for the whole phase including amber and all-red). If transit and parallel cars are permitted, the minimum green increases to somewhere in the ballpark of 7-12 seconds (depending on how you interpret various guidelines). And finally if you permit transit, parallel cars and pedestrians, then your phase length is determined by the pedestrian clearance time (Minimum Walk+Flashing Don't Walk). With a narrow side street such as those along St Clair, the Flashing Don't Walk is pretty short so allowing pedestrians only adds a couple seconds compared to just allowing vehicles. But with massive side streets such as those along Hwy 7, the minimum pedestrian time could drive the minimum greens well over 30 seconds, translating to minimum phase lengths as high as 40 or even 45 seconds.
The downside of phase insertion is that it reduces the total vehicle capacity by increasing lost time, and can put the signal out of coordination by adding time in the cycle. Inserting a very short transit-only phase has a fairly minor impact on coordination, since 12 seconds can be recovered fairly quickly at most intersections by shortening subsequent phases. But it has a larger impact on vehicle capacity since those 12 seconds are completely unused with respect to other road users. Conversely inserting an all-movements phase has a fairly low impact on lost time (just the extra amber and all-red), but with a long phase it can totally throw off signal co-ordination. Adding a 40 seconde phase in an 80 second cycle puts a signal at the opposite offset from where it should be.
Phase insertion is used at Lakeshore and Spadina. If there's a streetcar waiting or approaching at the end of the left turn phase (remember that left turns follow transit normally), a second north-south phase is provided with a minimum green for transit and cars (but not pedestrians). Unfortunately this feature doesn't address the main cause of delays at the intersection, which is the extremely long east-west phase for Lakeshore Blvd that streetcars are not allowed to shorten.
Phase rotation is where the order of the phases is changed to adapt to approaching/waiting transit. So with leading left turns, if there's a streetcar waiting or approaching at the point where the left turn phase would normally start, the order is switched so that left turns are served lagging instead. Since the total cycle time is unchanged, the signal is able to stay totally in sync. The co-ordinated phase is served at the "wrong" time for that particular cycle, but at the end of the cycle it will always be back to normal operation. Similarly there is no impact on vehicle capacity since it's the same phases, just in a different order.
The main downside of rotation is that it can cause a very large delay to left turning vehicles. With phase insertion, the extra phase is kept to a minimum and so are delays to left turning vehicles. Adding a 12 second phase simply delays them by 12 seconds, which is not a big deal. But with phase rotation, the transit phase is served up to whatever length it was going to be served normally. Often that could be a very long time, especially during rush hour. Then you could start running into the issue of left turning cars building up in the lane and spilling over into other lanes.
Phase rotation is not used in Toronto, but it has recently become technically possible as a result of equipment upgrades.