Speed limits do not increase traffic capacity of a road.
Why? Because a 1 second interval between cars remains fixed, but the vehicle distance grows.
Discuss (unless you all agree with me, then answer with silence).
Sorry, but you are quite incorrect; so please avoid making such rash assumptions in the future.
The traffic capacity of a road depends upon several different variables such as: condition of the road, the design of the road, the number of lanes the road has, obstructions in the road, weather on the road, and so on.
One of the things that roads have is a design speed. Roads with a high design speed (such as Interstates) tend to have rather shallow turns, restricted access, multiple lanes, and so on. Therefore, Interstates tend to have about the highest traffic capacity and highest speed limits.
So in this case, one can reasonably argue that higher speed limits do increase traffic capacity because roads with a higher design speed are simply better suited to handle larger traffic volumes.
However, if one is talking a more abstract terms where the only variable is the speed limit, then if the given section of road has a higher speed limit, then that road will have greater traffic capacity.
Or using your figures, here is a sample of what I worked out earlier this morning ...
If one assumes:
An average vehicle length of 13.42 feet, and
All of the vehicles have the same length, and
All of the vehicles are one second apart, and
All of the vehicles are travelling at the speed limit, and
There are no other factors impeding the traffic (weather, accidents, poor road conditions, etc.).
Then, one gets the following:
For a 1 MPH speed limit, then the number of vehicles per hour is 354.6,
For a 10 MPH speed limit, then the number of vehicles per hour is 1880.0,
For a 20 MPH speed limit, then the number of vehicles per hour is 2470.2,
For a 30 MPH speed limit, then the number of vehicles per hour is 2758.5, and
For a 60 MPH speed limit, then the number of vehicles per hour is 3123.6.
So again, a higher speed limit works out to a great traffic capacity.