It's been brought up on a number of threads regarding race in WWE. As some others have already mentioned, there's probably no single, simple answer to the question.
If you look at the rosters of WWE, TNA, WCW, ROH and any number of companies active in the United States during territory days, the vast majority of stars have been Caucasian. However, there've been quite a few wrestlers of different ethnicities who've had successful careers in WWE.
*Pedro Morales was WWWF Champion once for nearly 3 years, Held the WWF Intercontinental Championship 2 times, held the WWF Tag Team Championship once with Bob Backlund, making him the company's first "triple crown champion" in its history.
*Mr. Fuji was a 5 time WWWF/WWF Tag Team Champion, 3 times with Toru Tanaka and 2 times with Mr. Saito.
*The Wild Samoans were 3 time WWF Tag Team Champions.
*Tito Santana was WWF Intercontinental Champion & WWF Tag Team Champion twice each.
*Yokozuna, real name Rodney Anoa'i, was a 2 time WWF Champion and 2 time WWF Tag Team Champion with Own Hart.
*Kofi Kingston is a 4 time WWF Intercontinental Champion, 3 time WWE Tag Team Champion and a 3 time WWE United States Champion.
*Rey Mysterio is a 3 time World Champion, 2 time WWE Intercontinental Champion and 4 time WWE Tag Team Champion.
*The Rock's career speaks for itself as he's a 10 time World Champion, 5 time Tag Team Champion and 2 time Intercontinental Champion.
Granted, not all of these wrestlers have been main eventers, but so what? Look how many Caucasian wrestlers have been through WWE over its history and didn't make main event status. You also have to take into account ethnic populations of the United States as some 72-74% of the population of the United States is Caucasian. Since nearly three quarters of the United States population of roughly 318.5 million people is Caucasian, it's not illogical to reason why most of the roster of WWE and most other companies in the United States in any industry, for that matter, is comprised of Caucasians. In Japan, only 1.5% of the population is made up of foreigners, which means there are considerably fewer Caucasian wrestlers in Japan than native Japanese wrestlers.
Pertaining to Asians, or racial minorities in general, one thing that's beyond doubt is that WWE has relied far too much on characters or gimmicks supported on cultural stereotypes. It's something that they've moved much farther away from in recent years, though I don't believe some of them can be interpreted as being intentionally offensive. Take Los Matadores as an example; two young men of Hispanic/Latino descent dressed in gaudy, colorful ring gear while wearing colorful masks over their faces. Is it a cultural stereotype? To some degree yes because that their ring gear looks similar in design to the costumes worn by matadors. At the same time, however, the fact that they're dressed in gaudy, colorful ring gear while wearing masks is dirt basic description of probably 70% of Mexican wrestlers.