There's an easier solution. A vehicle weight tax that actual laborers are exempted from. Weight is what damages the roads, so a weight tax would accomplish practical and ideological goals.

You could do that, but in southern states they’d just make it too easy to get the permit. See Oklahoma’s “commercial vehicle” loophole where everyone has their car zoned commercial to get a tax write off. Also electric pickup trucks are a thing.

Hot take: Let people enjoy what they want. Hypercars and planes are much worse than pick-up trucks.

If you want to buy a second smaller car that's fine, but just don't do it because you think it'll help the environment, because it'll actually have the opposite effect. Producing a car takes a huge amount of energy and creates a huge amount of carbon pollution and other waste. The amount of gas (and thus pollution) you'd save by using a new small car will never come close to making up for the pollution that was created in the production of that car.

The most environmentally helpful choice is for people to keep using their current car for as long as they can, no matter how much gas it guzzles or oil it leaks.

With that said, life is of course much more complicated than that, so it shouldn't be the only factor you consider in deciding whether or not to buy a new car.

EDIT

To the couple of people who downvoted this, I'm not just making stuff up, this is information I heard from scientific sources. Here's citations:

https://www.scientificamerican.com/article/when-used-cars-are-more-ecofriendly/

I went and looked up the metric equivalent. That's 8.5 km/l or 14 l/100 km. That's honestly disgusting.

Especially disgusting when you know most people with an F150 use it 90% of the time to go to work, alone, without any 6m rebars in the bed and would be better served by a Yaris that can do 20-25 km/l (ie 45-60 mpg)