London's Victorian Hyperloop: a pneumatic railway beneath the capital (2013)

For subway style intra city transit the rapid speeds and acceleration are hardly useful since you have many short travel segments. It’s a non starter there.

For inter city travel, the biggest challenge is getting right of way and building infrastructure between the 2 cities. This is hard enough to do for regular HSR, which has far more tolerance than the hyperloop vacuum tube would. It’s not clear how one would solve that for the hyperloop.

1) Move the air at the maximum speed of the cars. This optimizes for that speed, but increases wear on the brakes and total braking distance by putting forward pressure on the train as it slows down.

2) Move the air at some average speed. Now you increase overall energy consumption having to fight (some) drag, while also having (slightly) increased brake wear and stopping distance. Nobody wins here, and you'd need to do a lot of fancy maths to figure out the right balance between energy consumption of the train and air-moving fans versus energy consumption of creating and maintaining a vacuum.

Alternatively, you could get crazy complex by having something like blast doors sitting between different zones (acceleration, top speed, deceleration) that automatically open and close, and try to create loops of air at different speeds and directions in each of the sections. I'm not even going to bother guessing how difficult to safely operate or how efficient such a system would be.