Earlier quoted context omitted.
Only reason they wouldn't take off outside China is the astronomical tariffs the West are putting on Chinese cars (100% in the US). Though depending on the wording, they may be able to just build a plant in Mexico and take advantage of NAFTA. I can't tell from the whitehouse post on the tariff if it's tied to country of the manufacturer or just country of origin (usually it's origin).
Or if the build quality of their vehicles was not up to par with US regulation or the quality standards the US market is accustomed to..which seems very possible given the connotations generally shared domestically around the phrase “made in china”
You get what you pay for.
In the case of electric cars, China has their own domestic market that actually wants to drive a decent car, and so they are building for that.
BYD cars aren't particularly "cheap" in the way a "Made in China" spatula is.