We should spend more time and energy improving pedestrian and cycling infrastructure and stop the growth of urban sprawl which makes you incorrectly think you need to solve this problem. A great book on this topic - Carmageddon

I think it is a great way to save money and help the environment.

The big problem I see is security / trust. But you have that risk with rideshare.

Carpool is perhaps the only means of commute that offers no timing flexibility. Unlike public transport or driving/cycling alone. I would think, its a rather small market preferred by people with shift jobs or state/federal employees who don't can't stay a minute below or above their office hours.