Things like this exist in New York, although they're significantly more... informal. Two dollars, cash.

http://projects.newyorker.com/story/nyc-dollar-vans/

Leap can be faster because they cut a lot of things that the SFMTA buses provides. A big delay on the public buses is letting people with wheelchairs on and off, if they are using the same design as the video it looks like they don't support that. They can also cream skim the most popular routes - SMFTA is sort of obliged to offer at least some route going near most places, regardless of whether that gets them anywhere quickly.