Kei cars are quite cheap to buy, but most are somewhat "built down" to hit those low price points. The quality of assembly is fine: they're Japanese industrial products, after all. But the design itself is not aimed at a long service life. Japanese consumers don't keep cars - particularly kei cars - a long time, and that's largely because the frequent (and expensive) mandatory "shaken" inspections stop making sense for older, depreciated vehicles. They just junk/recycle them and get a new one.

That's why you see prices no more than the equivalent of a few hundred dollars for used kei cars that are old enough to require yearly shaken inspections. Along with the expensive inspection fee itself, those inspections are meticulous and inevitably spot things that need to be fixed (or they won't pass the car), necessitating repair expenditures. It quickly becomes a case of throwing good money after bad...and the cars aren't designed to be long-lived, as that would constitute production costs the market sale prices wouldn't sustain (it's a very competitive market in Japan).

Honda's kei car offerings are a bit of an exception, with models like the N-Box being designed for a longer service life and priced a bit higher. They have a following in the kei car market, but it's not a strategy that every kei car manufacturer has available.

The American vehicle consumer won't accept the rapid depreciation associated with comparatively short service life, even for something with a low initial list price. They are also likely to be concerned with safety in accidents. Studies in Japan have shown, perhaps surprisingly, that kei car rates of death and serious injury in accidents are actually almost identical to other passenger vehicles (they have airbags and structural reinforcements, etc.). However, Japanese speed limits are lower than in the US, and kei cars have a higher percentage of their total mileage occurring in (slower) urban driving. That would reduce the speed and thus severity of collisions, contributing to that relative parity. Speeds are higher in the US, which would likely drive up the injury rate a bit, but it's probably the perception of a lack of safety that would be the real problem.

Kei cars, for the most part, would also struggle with the higher average highway speeds in the US (to say nothing of Europe). The 50mph or so of a Japanese highway is no problem; the 70-80 average speed on a US Interstate is about as fast as they'll go. They'll do it...but would feel like you were pushing the tiny engine awfully hard.

All-in-all, I like the idea of legal kei cars in the US, but the existing models would require some re-engineering to succeed in the US market. Currently Honda, Toyota subsidiary Daihatsu, Suzuki, and Nissan/Mitsubishi (NMKV joint venture) make them; Mazda has rebadged Suzukis available and Toyota and Subaru have rebadged Daihatsus. I'm not sure any of those makers would be keen to take the huge risk of re-designing products in a way that might make them less profitable in their domestic market or producing separate, US-targeted models.