This is an interesting question. If the restriction is based on parking space, the suggestion of off campus parking could work. If it is a matter of simply wanting to create a culture where frosh stay on campus, there could be a change. Regardless, if it’s important to you, I think you will be able to find a workaround.
With that said, make sure your son is truly prepared for this, especially if the car is a little difficult to access. My kid has had a car on campus - but in a somewhat inconvenient lot - for the last 3 years, and has had occasions when he has gone to use it and found it had a flat, was snowed in, had collected tickets (because a requirement to move for maintenance had been posted in the lot he had not visited), etc. Probably all worth enduring if it’s about a way to leave in an instant but frankly, not the hassles most of us considered at the outset.