After having lived in Russia for a bit, I'm mildly surprised that a US equivalent of Marshrutki [1] haven't really popped up in US cities. While St. Petersburg and Moscow have really well built out public transit systems, the urban sprawl and construction of the cities just doesn't allow for access by anything but non-bus-sized vehicles. The tl;dr of the wiki link below is imagine a passenger van that runs a fixed route - you can board or exit anywhere along the route by signaling the driver, and while slightly more expensive than public transit, you get the benefit of flexibility.
Here in SPB the marshrutki usually run parallel to major routes for a bit then deviate to hit residential areas or give fast-access to shopping centers, and combined with public transport you have just about everything you need to get around fast and conveniently. I suppose that such a system would suffer from the same issue of "everyone already has a car" that public transit in the US does, but it's a nice trade off.
(An aside, it's also a thrill ride each time, but when you need to get 10 km in a few minutes and have no care for your well-being, it's the best way to travel)
[1] = https://en.wikipedia.org/wiki/Marshrutka