> People don't want to spend their commute with random people who just happen to be going the same direction

Many, many people already do this on public transport. What we're talking about is general door-to-door public transport.

Car-pooling is awkward to arrange, particularly for short joined parts of the journey (e.g. picking someone up part way and dropping them off a little later), and it's extremely hard to arrange anything that overlaps such that the first passenger needs to get out before the last passenger (currently would involve handing over the keys to your car).