Cars blocking intersections and/or sidewalks can easily be solved with automated traffic fines - that's how Zurich and London does it (the former without any congestion pricing!)
Many cities also have special lanes only useable by some classes of vehicles - e.g. busses (or sometimes taxis as well) - I guess ambulances could also use those.
In fact, congestion pricing doesn't solve any of those problems, it's just an irrelevant (as in, it doesn't solve any specific problem directly) regressive tax to "drive less".