Many alleyways are currently being utilized as low car traffic bike routes. If those alleyways were prioritized for bike traffic and marked as such they could make for strong bike corridors. That doesn't mean we should stop adding bike corridors to more direct roads though. Encouraging bicycle use is a top way to reduce gridlock!
Having said that, the best way to reduce traffic on main roads is to get people out of cars. That means bicycling and transit use has to look like an attractive alternative which means driving has to look unattractive. Right now our society is set up to emphasize driving and deemphasize taking the bus/T. We need to switch those or else our city literally will not have the road space to grow.
I'm excited for the BRT that will connect all of Oakland, Shadyside, and East Liberty with downtown. It makes for an extremely easy connection between the T to the south hills and the BRT to all neighborhoods east. The P1 is already a super fast connection to Lawrenceville although the 91 is the route that reaches more of the neighborhood.
I think we need to build a lot more support for transit before we can start making serious infrastructure investments. Our city needs to be a lot more dense before rail makes more sense than super fast buses. In Pittsburgh the busway is actually faster than the T due to speed restrictions.