That is a possibility. But I imagine that when driverless cars become ubiquitous, most people won't own them.
If you did want to pay for a car to swing by your house to pick you up, it probably wouldn't be a car, but something more like a small bus with sleeping compartments that could pick up and drop off people along the way.
If you could fit 10 people along most of the route (and you could assuming it was between 2 moderately populated areas and road trips were as common as they probably would be), your passenger miles per gallon would be incredibly high.
Given that this doesn't happen today and that subtracting the cost of the driver isn't going to reduce the overall cost of such a trip significantly, I really don't see that happening. The biggest benefit for bus-like operations is not needing to have driver rest time, but lack of flexibility is still going to push people to their own private transport.
Combine driverless cars with maglev trains that can combine multiple cars into one long train with individual cars coming and going, and you may have something. I'm not holding my breath that I'll see anything like that in my lifetime. Transportation infrastructure in the US has gone nowhere in my nearly 40 years; I don't expect a great deal of change (to the infrastructure) in the next.
> subtracting the cost of the driver isn't going to reduce the overall cost of such a trip significantly
I'll calculate the costs 10 passenger van, if you could work it out so that it gets an average of 40 mph for say 20 hours out of the day. That's about 300,000 miles per year divided by 20 miles per gallon that's 15,000 gallons of fuel. At $4 dollars per gallon thats $60,000 per year in fuel costs.
I'll assume another $60,000 per year in maintenance and depreciation (this is probably high b/c you can buy a new large passenger van for under $30,000)
We're at $110,000 in variable costs so far.
Now at $30,000 per year per driver in total costs (could be less, could be more depending on area)
Driver works 40 hours per week with sick time and vacation time. You'll need around 5 drivers in order to keep the van operational 24 hours per day.
That's $150,000--more than half of the total costs.
There are also other factors to consider. Drivers, don't want to operate that far from home, so you have to pay more.
You have to set up a logistical solution so that you can refresh the driver every 6-8 hours. That means depots where you can exchange them.
If you did want to pay for a car to swing by your house to pick you up, it probably wouldn't be a car, but something more like a small bus with sleeping compartments that could pick up and drop off people along the way.
If you could fit 10 people along most of the route (and you could assuming it was between 2 moderately populated areas and road trips were as common as they probably would be), your passenger miles per gallon would be incredibly high.