The same capability currently exists independently of driverless cars. What makes you think the utilization of this tactic will change with driverless cars?
Coordinating this is a hassle. With driverless cars, you could say "I need a vehicle to take me from A to B" and a vehicle just shows up, possibly with one or more passengers who were already enroute to B. It wouldn't surprise me if that becomes the norm with an option for "I require a private trip" for an extra fee.
I currently have two apps on my phone that provide me a way of saying "I need a vehicle to take me from A to B". Both have attempted to do what you are talking about, but have settled on something more similar to "Walk to checkpoint A and wait for 5 minutes and you'll be dropped off at checkpoint B that is kinda close to where you actually want to go".
As it turns out, coordinating rides is pretty difficult, even with sophisticated software doing a lot of the work for you. Maybe if either of those companies had huge market shares, then maybe the problem gets easier. I'm not counting on it.
Not sure where you live but I agree with shoyer that Lyft Line and Uber Pool serve this functionality very well in San Francisco, New York, and presumably also the other major metros where they've launched it (Austin, Boston, Chicago, Los Angeles, and Washington, D.C for Lyft Line)
Taxis are expensive and public transport isn't as convenient. A minibus taking me from within a block of my house to within a block of my work would get my business.
Labour costs are a significant part of any such operation, where I live at least.