There's definitely something to that. IIRC some municipalities partnered with Lyft on "last mile" transport from regional train services. Makes a lot more sense than park and ride, but I'm not sure what ever happened to it.

I'd argue that there's no reason transport agencies couldn't do this kind of intelligent routing/hailing themselves. The problem is usually that government is actively punished when they don't go for the cheapest possible alterative, so rather than hire a team of skilled, innovative developers, they out source to a lowest cost bidder. As a result it looks like private enterprise is the only place where innovation happens. It's a shame.

IIRC, Switzerland actually has some on-demand minibus routes. Basically, you have to call a number N minutes in advance, and the minibus will show up. This could easily be appified as well (and maybe it already is today, it's been a while).

I think that deserves consideration, along with the related category of access-impaired riders. In a major city it might easily be cheaper to pay for years of door to door service than make an ADA retrofit for a subway station in an old building.

Why can't the city just run smaller vehicles, like minivans or airport shuttles, on less popular routes? Sub-contracting may be cheaper for the city but would make for terrible PR. Since driver salaries are the biggest cost, the only way private companies could make these routes profitable is by doing the very same things Lyft/Uber are criticized for: low wages, no benefits etc.

EDIT: Reading some of the other replies, I suppose making rides on these routes on-demand instead of fixed timetable services may change the economics of less popular routes.