[amrcnimgrnt]

"A car needs several car-lengths of space between them."

The distance between bumpers actually cancels out (actually it comes out in the car's favor). First notice that in the picture the cars are almost touching, so clearly you mean in fast moving traffic.

In fast moving traffic the carrying capacity of a lane is equal of the inverse reaction time (typically engineers use a large margin of safety and 2 seconds is used -> 1800 cars/(lane hour)).

For bikes, since they travel more slowly, you have to add the time it takes to travel their own length. So the carrying capacity of a lane is 1/(reaction time + length of bike / speed of bike).

The "several car lengths between them" is literally space that exists only because cars have generated themselves by virtue of going very fast (since fast moving vehicles get to where they want to be quicker and therefore get off the road to make space for someone else).

This doesn't mean that cars make sense in dense cities. They don't.

This doesn't means cars don't take more space by virtue of being longer in slow traffic. They do

But it does mean that, if there are "several car lengths between them", they are in fact operating in a more space efficient regime.