I have long thought that if it is a truck/SUV it is for use in situations where you don't care about dents and paint scratches and thus those are not factors in the value. Dealers and car rental places would quickly figure out that they cannot legally look for such things, but customers will find a reason to buy a different one and so they would stop leasing or renting trucks/SUVs. They may still lease/rent truck/SUV shaped objects, but they will count as light cars for MPG purposes and so cost a lot more.
Other countries can be good examples of policy that functions well. First and foremost, they should be included in the average fleet mpg rating for vehicle manufacturers. This is because they are a part of the fleet of vehicles produced and contribute a good sized portion of the greenhouse gasses emitted from vehicles. They are also one of the biggest number of vehicles sold so they shouldn't be exceptional.
I like your idea but I feel it is too in the weeds for simple policy.
Effective policy would drive the truck engines and size to be more efficient, because they can but do not. They aren't because of the exemption. Plenty of trucks globally are significantly smaller than ours and get the jobs done. Generally I agree a more efficient car is likely ideal and should be policy enforced.