True. But “dead” parking time is insanely cheap in most situations. It doesn’t cost me anything to keep my car parked in my driveway. Almost all of the cost of a car - fuel (obviously), depreciation, maintenance/repair, tolls, even most of insurance - comes from using the car. Not from dead time. So deadheading increases the overall cost of driving by a material amount, while parking does not.
The most obvious exception to that is when parking is expensive. If you’re living in or travelling to the central business district in an urban area, parking can cost a fair amount. But those are the exceptions - the U.S. pays less than $85 per year in actual parking outlays per vehicle, which is trivial compared to the other costs of the vehicle.
Worse for TaaS’ prospects, self-owned autonomous vehicles will reduce parking costs. Sure, if I have to pay $300 a month for my downtown parking space, then that really tilts the playing field in favor of TaaS instead of owning my own autonomous car. But if my car is autonomous, I can just have it drop me off and head a half-mile or so out of downtown to a much cheaper parking area. There’s still some expense for the cheaper parking lot (and a tiny deadhead), but parking expenses even for dense urban cores will fall.