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.