There are plenty of small cars made outside of China. Why do you think not a single auto manufacturer worldwide bothers to export their best selling models to the US? The market here wants SUVs and trucks, not $15K subcompacts.
Outside of Chinese-made vehicles the US has probably the most open auto import market in the world. Most manufacturers enjoy a 2.5% tariff, which is a joke, and not reciprocated anywhere in the world. All these foreign manufacturers are selling $25-50K+ cars just fine (over 4 million of them every year in fact). It's the US market that is rejecting lower priced cars.
higher sounds like a quality argument, which may be true. they are not stricter though, which is what they'd need to be to refute the parents point. take headlights, for example, where the us's requirements are significantly stricter than european ones.