His biography explains a lot of why he seemed to have been welcomed with open arms by that notoriously closed city, Kyoto-- where one hears the Japanese won't rent to other Japanese unless their families are known to each other. Taught at Harvard, writes for Time- by all means invite him to a closed Buddhist investiture ceremony. Timing may explain some of the rest. In 1991 Tokyoites at least were tired of the wave of unilingual brash foreigners, but the golden years were within living memory; they may well have been current four years earlier. In the early 80s, and even more the 70s, foreigners didn't go to Japan to get rich. There had to be a hook that connected them to the place, which saved them from some of the unlovely attitudes of the English teachers.
In the end it might be no more than personality. Introverts and melancholics do not fare well in that cheerful extroverted culture; a liking for, indeed a need to be in, other people's company, and a tendency to take things lightly puts you smack in the culture's mainstream and makes you congenial to the Japanese themselves. Helps that Iyer grew up a perpetual outsider, which is about the only way to survive happily in Japan. And of course he's a reporter, and edits his experience; which saves him from the petulant ego displays of books like The Inland Sea or The Roads to Sata-- both of which, note, are about gaijin during the golden age who were still sulky that the Japanese refused to be the way they wanted them to be.
(I see Richie died two months ago. Wikipedia notes "Although Richie spoke Japanese fluently, he could neither read nor write it proficiently." I suppose I respect someone who can travel in a country where he can't read the names of the train stations; I couldn't do that.)