Highways didn’t exist when cars became common. They came because of cars. We never took them away from horse riders. We gave car drivers a new option.
This would be taking something away from drivers. And that’s what people hate. Look at the responses to congestion taxes or toll roads. Or even traffic jams!
People behave as if they have a right to use any (seemingly) public road just because they have a car. Even private toll roads.
It’s not feasible.