In practice, the places with lots of traffic congestion are dense enough to have transit going to/close to the areas with lots of demand.

That's why buses have more than one stop on their route.

And that's why it can take 40 minutes to travel 4 miles.

I'm assuming you live in San Francisco? As a visitor, it seemed to me that this was more due to the insane car-bus road-sharing conflicts, the inability of Muni buses to accelerate up a hill, and the deluge of 4-way stops.

Nope. Chicago suburbs, actually. But that's how long the buses take out here in the suburbs, and how long it's taken me in downtown Chicago before. I don't go on the buses that often, and this is one reason why.

The buses can have 20-40 stops in those 4 miles, mind you. I don't mean it's all due to traffic.

Then it’s much more efficient to cluster those 100 different places into a few compact areas, so that most of the people can walk or bike, or take the subway.

The problem is when those 200 people want to go to 100 different places spread throughout hundreds of square miles of evenly low density suburban sprawl like a modern US metropolis.

> Then it’s much more efficient to cluster those 100 different places into a few compact areas, so that most of the people can walk or bike, or take the subway.

Absolutely. But there will always be people who want to get to locations spread all around even a metropolitan area (as well as further-flung locations around that area), and while it's possible to build a public transit network to get them there, with enough throughput to cover the volume of people, the latency will still be worse than a point-to-point trip directly from point A to point B.