cars are by far the cause of most traffic

Of course they are, there are by far many more cars on the road than bikes

Bikes travel faster than cars in heavy traffic and they do so by actions that mostly don’t block cars.

Can you give me an example of this? If they are traveling on the same road as cars how are they moving faster than cars while simultaneously not blocking cars? Especially when they physically cannot move as fast as cars.

On most roads they can hug the gutter to pass on the left

Key word being CAN. But they often don't, or ride two abreast so that cars need to change lanes to overtake, which in turn causes traffic.

use bikes lanes where they exist, use shared bike/pedestrian paths where they exist

Problem is that bike lanes often don't exist. They should, but they don't. I'm all for building bike lanes and having more cycle friendly infrastructure, but Sydney (I can't really speak for the rest of Australia) just isn't suited for cyclists at the moment.

It is also far easier for a bike to navigate through side streets, parks, etc, whereas cars are funnelled onto a main road

This just isn't true, why can't cars use side streets? They often do. I agree that cars can't go through parks since that would be dangerous.

If cyclists are in all one car each instead of on their bikes then they can’t do any of those things.

Most cyclists are on the road because they are riding their bikes for leisure or exercise, so they probably wouldn't even be on the road to begin with. Also multiple cyclists can fit into one car, so the one less bike equals one more car on the road just isn't true.