Yes, CAFE standards work. When we force manufacturers to make vehicles that get better fuel economy they do. They don't focus on fuel economy on their own because fuel economy isn't important to US new car buyers. Buyers will routinely pay more for a larger, more powerful, and quicker vehicle. More recently they will pay more for AWD and larger touchscreens. They won't pay for better fuel economy
The increase in US vehicle fuel economy is best shown graphed on top of other vehicle traits. Fuel economy is increase is combination with massive increases in power and weight of vehicles.
(I'll add that in addition to vehicles getting larger, more powerful, more technologically advanced, and more efficient - they are also cheaper to buy today than 40 years ago adjusted for inflation)
From the 2022 Automotive Trends Report