In practice however that hasn't really been borne out: the city's buses are notoriously slow. The city has (correctly) reprioritized bus lanes (including lane enforcement for scofflaw drivers) and express services (SBS) in response, but at that point we're essentially back to rights-of-way (i.e. how much of Europe runs timely and efficient streetcar networks).
In short: I think streetcars would be less effective if not (partially) separated, but more effective otherwise. Given that the city is moving towards bus lane separation anyways, I personally believe they should revitalize the streetcar network instead. But that's (1) expensive, and (2) involves impressive amounts of local political spaghetti, given that the buses are currently run by state-level MTA while the roads are owned by the city.