Private transit as you propose can only exist in suburbs where everybody has large lots, and will be more expensive than owning your own car. Those private cars will always take up a lot of space per person.

If you live someplace where you take the shared tram for the vast majority of trips, then what you propose can work for the few trips where you the tram doesn't work. How often do you really need the private space? If it is all the time you have agreed to forever live in suburban sprawl, with potentially long commutes.