I'm more familiar with this model popping up in large developing-world cities that have exceeded the capability of governance to provide transit, e.g. much of Africa is like this, with a host of small independents each running their own routes.

The two main issues they encounter, which are related to being private and decentralized, are that routes collect around a few hubs(e.g. "downtown" or "hospital") that guarantee customers, but get vastly over-serviced without a corresponding cross-town option; and they don't have a dedicated right of way, and end up fighting through the city traffic, sometimes getting stalled for hours by uncontrolled, massively over capacity streets.

There is a lot of room for technology to improve on this - if the governments got into the picture and ran a minibus app, they could track and subsidize those services to formalize it, encourage use and reduce inefficiencies, allowing a transit grid to be formed with little formal capital.