A taxi, robot or not, will never be able to meet peak demand... they'll be provisioned to meet 60-80% of peak demand and surge peak pricing. That's the key part of the robot car business model -- these companies want to soak you for using public infrastructure.
The Musk tunnel thing is totally different, it's an extreme version of Washington Beltway congestion pricing that charges you $3-60 to waste less time in express lanes.
If sitting in rush hour becomes even easier (and even more profitable, if you can work while going to a meeting), we'll have more of rush hour sitting.
It's enough if just ~20% of those who participate in traffic are doing so with a "self driving car", if they otherwise would have opted not to do so, we'll have even higher peaks.
Surge pricing might not matter much, because it's in the interest of the fleet operator/owner to get maximal utilization, to get maximum profit. After all Uber does surge pricing to motivate more drivers to come online, but if you have a constant supply (constant number of self-driving cars in the fleet), then you can simply use it to maximize profit. (Or to manage perception, ie. to show that yes there are cars available, sure, it comes at a high price, but they are "available".)
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> these companies want to soak you for using public infrastructure
Yep, US cities are so burdened with problems (a nasty set of incentives) that public transit is non-viable, which drives even more subsidization of the sprawl, which then breeds these companies that try to "solve it". (I mean Uber/Lyft successfully increased the supply of taxis, which drove prices down. Yaay, great, but this just meant more congestion, more pollution, more sprawl, nothing fundamentally solved.) And of course at this point properly pricing externalities is an insurmountable political challenge, because people are so wedded to their way of life.
Which might be okay if throughput is kept high, and folks can read/eat/sleep while ij traffic.