I don't think this is a crazy take, but it is missing two big factors that self driving maximalists often ignore.
First is the cost of driving. A reasonable rule of thumb is $0.50/mile all in (i.e. including depreciation, repairs, gas, etc) -- you can get down to half that pretty easily and maybe a little lower, but especially if you're spending tons of time in this car you're probably going to want a nice comfy one, which will cost more and depreciate faster. So, these trips you're imagining everyone taking constantly are not going to be accessible to most people. Cars are already the second biggest expense in most Americans' budgets, one which scales with mileage, and which self driving would only increase (have to pay for the lidar, on-device compute, whatever remote service handled edge cases, etc).
The second thing your predictions miss is geometry. Despite the decades of predictions about self-driving cars being able to run safely at much higher speeds and with much tighter tolerances than human-run cars, the tyranny of geometry and stopping distances (which actually won't change much even with millisecond reaction times) means that throughput of car lanes is unlikely to change much (though we could all imagine top-down infrastructural changes helping this a lot, eg coordinated self driving cars and smart roads, those seem unlikely to land anytime soon given American political inclinations). Imagine how spaced-out people are on the highway -- in each lane, 1.6 people (average car occupancy) every football field (300 feet -- safe stopping distance at 70mph). If you're trying to go anywhere more densely packed than that -- e.g., a city, a restaurant, a ball game -- you're going to start to run into capacity constraints. Mass transit, walking, and cycling all can manage an order of magnitude higher throughput.
So while I think your prediction -- that self driving cars will increase demand for road space -- is right, the valence that takes for me is much more negative. The wealthy will be able to take up way more space on the road (e.g., one car each dropping off each kid at each extra curricular activity), condemning the poor to even worse traffic (especially the poor who cannot afford a self driving vehicle, who will not even be able to play candy crush while they're waiting in this traffic). People will continue to suburbanize and atomize, demanding their governments pay for bigger and bigger roads and suburbs, despoiling more of the areas you'd like to hike in, with debt that will keep rolling over to the next generation. Bikes and peds will continue to be marginalized as the norm for how far apart people live will continue to grow, making it even more impossible and dangerous to get anywhere without a car. I hope I'm wrong but this is how mass motorization played out the first time, in the post-war period, and if anything our society is less prepared now to oppose the inequitable, race-to-the-bottom, socialize-your-externalities results of that phase of development.