So if there are two routes from A to B and one is longer, then the shorter route should be reserved for the modes of transports that have a higher capacity. (That usually means banning cars)

Another really good option is to have dedicated bus lanes so buses don't get stuck in traffic.

As a car driver you massively benefit if other people take the bus or bikes instead of their car. Plus you and especially the ones who are to old, young, poor, disabled to drive a car have good options of getting around.

Well, you don't have infinite money, or space. Adding a bus lane and a car lane clearly will add more capacity than doing just one of them, but adding a bus lane will likely reduce traffic so much in the other lanes that you don't even have to add another car lane.

And adding just a car lane means people would rather be stuck in their car, than stuck in the bus, in the same lane, and we have tragedy of the commons.

So adding a car lane just means emptier busses, but same slow traffic. So what value did adding the lane add?

It'd just be government waste.

The first is true, but the second doesn't follow. For a bus lane to make a difference you need more than a lane, you also need good bus service using that lane. Bus service in many cities horrible and so nobody sane will ride it. A lane of empty buses running around helps nothing. If you propose a bus lane you need to do it with all the service that will happen so we can evaluate it.