Public transport is not run at a loss as a form of wealth distribution, it's run at a loss because the impact on the economy/society via enabling people to move around more freely is not captured via ticket prices.

It's no different from building roads or sewage systems - you don't try to directly capture the building cost from the people using them because the higher order benefits from having a healthy, growing, functional society (both in the general wellbeing of the population, and in tax revenue) outweigh that.