No, but a more reasonable level of regulation like the EMA uses would make things a lot better. There are levels of regulation between Anarchy and Stalinist 5 year plans.
For emissions, but not for safety. My understanding is the NTHSA does not actually approve a car for sale in the US, it just requires that the manufacturer certify it meets the regulations.
Your car needs to be certified to not spew shit everywhere in the same way your drug needs to be certified to not harm people who take it. For obvious reasons, one is far more expensive to test and certify.
Is the food in your local supermarket certified to not harm people to eat it? It's regulated, and the FDA can inspect to verify compliance with regulations, but suppliers do not have to get approval from the FDA to ship.
The problem here is the scale of harm and manufacturing of inert or ineffective products, not even too mention harmful ones. This is why every formulation has to be approved.
GMP etc. Requirements have been added after some scandals with tainted stuffs making people sick instead of better.
This would be not compared to mom and pop food stand but a big supermarket chain or food manufacturer.