I see this all the time and I just do not believe it is true. Uber/Lyft/etc undercut taxis for users to take market share, and have drastically raised prices to become marginally profitable.
Autonomous cars are more expensive, and the labor in non-autonomous cars is not the majority of the costs. In NYC, a 1hr Uber could easily cost $100 against a minimum wage of $15.
The idea that a taxi trip becoming cheaper than a car owners marginal car trip would require dramatic dropping of taxi prices. Even halving is not really going to do it, and I don't think removing the driver even halves the costs.
The autonomous taxi boosters also seem to overlook what happens to unattended, unmonitored public infrastructure in urban areas of this country. The reason I stopped using Zipcar in NYC was because they were typically trashed inside by the previous drivers. Now imagine an autonomous taxi that gets turned over 10x as often. Good luck.
That doesn't mean I agree with the GP's point about it lowering car usage overall. The reduced cost of auto taxies also pushes against your reluctance to take one, though perhaps not all the way to "use my car whenever I leave the house" levels. I also think that once people begin replacing their cars with autonomous taxis, they'll sign up for all kinds of taxi subscriptions that will further reduce that reluctance. After all, driving your car now isn't completely free: it still costs you gas money, plus the hassle of actually driving it. And other forms of transportation aren't free either. So the bar here isn't 0.