[Request] How does the capacity of a railway scale with the speed of the trains on it?

So I was talking with someone about high speed rail and the hyperloop and it got me wondering about some stuff.

Trains, and vehicles in general, need to keep a certain distance from one another in order to leave enough space for the operators to be able to react in time if anything were to happen. The higher the speed, the greater this distance will be.

My question is essentially: We assume that as a train becomes capable of higher speeds, the line will carry more passengers from point A to B. But is there is a speed where the opposite becomes true? A speed at which trains need such long distances between them that the amount of passengers going from A to B actually decreases due to a decrease in the amount of trains being able to be on a track?

I tried doing some calculations myself:

Imagine a train does 100 km/h and carries 100 passengers over a railway that is 100 km long. I used some quick formules for cars (I know their stopping distances are going to be different, but it's an estimate) and found out that it would have a braking distance of 100 meters. It means that at any one point, there can be a 1.000 trains safely on the track. Each train carries 100 passengers, so at any one point there are 100.000 passengers on the track. They travel in 100 km/h, so it will take an hour for all trains on the track to reach point B. This means a 100.000 passengers will arrive at point B per hour.

Now another train does 1.000 km/h and also carries a 100 passengers over the same length of track. I found a stopping distance of 5.000 meters. It means that at any one point, there can be 20 trains safely on the track. Each carries 100 passengers, so at any point there are 2.000 passengers on the track. They travel 1.000 km/h, so it will take 6 minutes for all trains on the track to reach point B. This means 20.000 passengers will arrive at point B per hour.

Thus even though for the individual passengers the trip will only take 6 minutes, the capacity of the railway is only a fifth of what it used to be.

These are back of the envelope calculations of course, so I probably made some mistakes or some incorrect assumptions, hence I wanted to post it here to see if anyone could either confirm or refute it.