What makes people think everybody would be on the road at once? At any given moment most cars are parked.
Why do people keep saying society would collapse without a rat race? In this hypothetical societal scenario most people would still work, and a good percentage of those people would choose to work less since they now have less overhead to pay for. The mailmen, sewer inspectors, road maintence crews, truckers, linemen and other societal fabric keepers would still go to work with less stress and more life options thanks to their downsizing.
Unsustainable? Planet Earth can easily support 7 billion mobile dwellers, even with half of them burning gas everyday perpetually travelling. Even if those dwellings were poorly insulated sticks and staples, requiring constant heating in winter and blasting A/C in the summer to keep comfortable; less energy and resources is used/consumed per capita. Compared to the average dwelling each human lives in now, average dwelling counting from starving Africans to trillionares. The only people who say this is unsustainable are the global elites pushing for global human enslavement.
Nature being overcrowded? Maybe, with half the country living in homes with wheels; depending on how many people desire to be in nature we could have mobile abodes dotting grassy fields and filling forests. A market would spring up like AirBNB for RV Spots where people who want a more private nature can connect with still owning land and rent pads by the week, month or even year. Scenic parts of the country would have to welcome freedom parkers or else lose business.
Stores would have to adapt to the RV economy. WALMART might get into the RV park/RV service business and offer metered water and electrical hookups in their lots, pay by the hour/watt/gallon. Overnight parking would be a competition point between chain stores, imagine COSTCO or TARGET lots allowing overnight parking for example. The hospitality industry would have to adapt, imagine MOTEL 6 becoming RV PARK 6 for example.
Why would RVs and vans get expensive? Depending on the rate of "migration" at first there will be a demand spike for new and used mobile dwelling rigs. If anything the cost of new rigs and maintence on used rigs would go down due to economies of scale. Cost to acquire and maintain 12v appliances and RV-type systems would drop for the same reason, with much more choices and competition much like conventional house appliances and systems are today. RV innovations would be abound, bringing many of the comforts and ease of sticks-and-bricks to mobile dwellings. Insuring a mobile dwelling conventional to custom would be as easy as insuring a conventional house. Manufactures of conventional sticks-and-staples RVs would have to build RVs that don't start to fall apart after a few-weeks-out-of-the-year use, due to the new full-time mobile dweller class. The conventional houses left behind will see new uses to support the upsized RV economy. Land will be valued for what is is, and we won't see speculative bubbles grow to nationwide proportions.
In all likelihood the new class of mobile dwellers, now the majority would flip the "who crazy here" to the people still living in conventional houses. Tons of stuff that filled peoples conventional homes, much should and would probably be shipped off to 3rd world countries, some would move into peoples rigs, and unethically some gets lost to the landfill. The general population would be happier; crime, murder, and suicide rates plummet; and Americans see a new rennisance with the same kind of attitude the frontier people had in the 1800s.
For the most part, if half the population of the USA downsized from conventional homes to mobile homes; the general populace sees a net gain, and the human condition gets much better.