One problem with this is that a large part of the cost of running a bus is the cost of the driver's time, and a bus has one driver whether it carries 15 people or 60. So small buses are more expensive to run per passenger, and this means the government must subsidize more of the cost. However, this would be an excellent idea for some of our older cities where the streets are too narrow to allow safe operation of full-size buses. A lot of cities in New England are like this. In general, if there is enough population density to support buses, they run the full-size buses anyway, which gives a lot of motorists a bad feeling about buses.

You don't have to train a driver to use such a mini-bus, asther are nothing more than glorified passenger vans.

It requires a commercial driving lisence, at least in the western US. Phoenix uses rideshare vans, which are like municipal taxis for the handicapped and elderly. They have elevators to take on wheelchairs. Full-size buses are used otherwise.

This is quite common in Europe, both in order to get down narrow streets and for routes with fewer passengers. You do save on fuel and maintenance, but not on wages so it cost more per passenger.

In most European countries you need a bus driver's licence for all vehicles with more than 12 (or sometimes 8) seats.

Trams are another solution for very busy city routes. Because they are on rails they can fit through narrower streets.

Most cities have minivans available for the elderly. I'm not sure if it is subsidized or if it is solely paid for by the individual.

There are so-called "jitneys" that do something similar.