https://www.jdpower.com/business/press-releases/jd-power-2018-us-vehicle-dependability-study
The dependability record is based on 3 years data, Kia #5, Hyundai #7, Toyota #9, Honda #12. Recent data shows that these guys are pretty much equivalent (slightly better).
We own an old Lexus (not our first one) - and our own experience with it (as well as the previous one we owned) matches the JD Power statistics (where it consistently has been top 2). The Kia ownership so far also matches our experience. We had 4 Subarus and despite their reputation for excellence - we had many issues with 2 of the 4 - matching the less than great results shown in this survey. The reality is that quality perception usually lags 10 - 20 years behind the real hard data, that was the same for the Japanese in the 70s (where it was not until the mid-late 80s that people understood how good their cars are) and in the opposite direction for Mercedes and VW where their stellar reputation stayed with them despite the fact that the by the mid-90s they were making questionable cars (before recovering somewhat in Mercedes case, a little less so in VW's case).
I have many friends in the global automotive design community (there are several large company design centers around here) and we hear the gossip from within the industry - Kia and Hyundai started going on a global talent raid 5 or so years ago and this in combination with their operational stuff is starting to bear fruit. Honestly, it is hard to buy a bad car these days (Fiat is trying to keep things interesting, however) - and the Koreans make great cars today. These are not the days of the Hyundai Excel with it's flimsy construction anymore.
As for Japanese design being unparalleled - I would argue that Nissan makes mostly built to a price cheap stuff nowadays (I would buy Korean over Nissan 10 out 10 times if I had to choose), Toyota / Lexus is still good, Honda is still good (but unlike Toyota with Lexus, still can't crack the luxury market with Acura). Subaru has finally started to fix their headgasket issues from the EJ engines with the move to the new engine architecture, Mazda is making fantastic vehicles - so yes, the Japanese are making great cars, but so do the Koreans these days.