We already have this in downtown Houston but you don't get a Transit van.

Instead it's a little battery-powered multi-passenger buggy, covered with ads and limited to downtown.

>door --> van --> public transit --> van --> door

Still works like this but once you take the train or bus outside of downtown, then you're back on your own for the "last miles" except for a few other non-contiguous neighborhoods where they are beginning to add additional cells of this limited-area connector service.

This has been willingly subsidized by the major businesses in each service area, so it is free to use on its own, once you get onto the regular public transit though, then normal fares apply there.