[eythian]

I live and bike in Amsterdam, which also gets heavy bike traffic. The thing is, things still work more smoothly if you are in the bike lane. The signals there are tailored to you, and you can get a whole pile of bikes through a light change even though it looks busy because they pack much denser than car traffic. If necessary, bikes will take space from cars, but it's not usually required.

Also, the busier parts tend to be in places where it's not useful to go in the car lanes anyway, or they're already mixed-mode (in which case it's the car traffic slowing everyone down because they end up stuck behind one slow cyclist, but 20 cyclists are stuck behind the car.)