Rush hour traffic is so gridlocked that cars often can’t know if they will clear a light cycle, so fining would effectively just reduce to a stochastic congestion tax.
NYC does have some dedicated bus lanes, but adding more means reallocating more space from cars which is a political no-go without reducing the number of cars first. That’s what congestion pricing aims to do.
Fining for blocking intersection isn't stochastic. You simply don't enter the intersection if you're not sure you'll be able to exit it. You wait at green light. Simple. That's how people in London and Zurich drive.
Congestion automatically reduces the number of cars (because they literally can't get into the city!), without congestion pricing. If you reduce 3 lanes to 2, then... 2 lanes will be blocked, instead of 3, so there will be complete gridlock & congestion - for cars. But not for busses! So public transport will work, even thought private is gridlocked. Combine this with (1) - empty intersections - and busses can drive very well!