I lived in LA for a year, and the biggest hurdle I had with using public transit in the city was exactly this: that stations, especially for the newer metro lines, often were 2-3 miles from my starting location and destination. Using public transit meant that I either was already near a stop or had a destination immediately next to stop. In every other case, Uber/Lyft'ing through traffic was faster (and cheaper when you add the price to Uber to and from the stations).

So I think this idea has potential, though its eventual success will depend two things: first, whether the price of the last-mile via's can be kept low enough to make the diversion to the transit stop affordable, and second, whether the via's and the public transit can reasonably compete on timeliness with ridesharing services.