The problem will come from sales tax and import duties when you try to register the car in your home state. In most states, you need proof that you've already paid the sales tax when you bought the vehicle (and import duties if the car is foreign), and if you haven't paid enough to match your home state's limit, you will pay additionally to match. This is why people from Alaska get so pissy when they move to the lower 48, because Alaska doesn't have a state sales tax for vehicles, and all of a sudden they're paying thousands of dollars just to register their car in fuckin Idaho.

Technically what you're thinking about already exists on the southern border, plenty of people will buy Chinese cars in Mexico and then drive them up, and they're able to get around the blanket import bans that the US has. However, they then will still have to pay any outstanding sales tax, plus the insane import tax on Chinese vehicles, making the car more expensive. However, given how cheap the Chinese cars are produced, and the relative weakness of the Mexican Peso relative to the USD, it may still come out as a cheaper option, though I'm not well versed in the Mexican auto industry.