lemmata, your assumptions are of course, flawed. (intellectual exercise

)
"•All of the best players in China and Korea are participating in international tournaments and almost no Japanese players show up for international tournaments."
Plenty of Japanese players show up. It's just that the vast majority are beaten in the preliminaries and so it may seem that none show up.
"•The strength of the player pool in China, Japan, and Korea are equal."
It seems to me that the only measure we have, are won games, semi-final and final appearances etc. By this measure, Japanese professionals are simply weaker.
"•It is twice as hard to win an international title than it is to win a domestic title because twice as many top players compete."
This certainly seems to have a sizeable amount of truth to it.
"•Players believe that their chance of winning a given domestic tournament is double that of winning an international tournament. Therefore, when considering the decision to participate in international tournaments, players halve the prize money in their heads."
I don't know about this. I think that this is too simplistic. In fact, the more I think about it, the more the conclusion appears unjustified. If their chance of winning an international tournament is half that of a domestic one; surely they would just halve their expectations.
"Is it any wonder that the top Chinese pros are so fierce in international competition? Winning the BC Card Cup could earn a player as much money as he would by winning the Tianyuan (a major title) 50 years in a row. Is it any wonder that the top Korean pros focus on international competition? Even accounting for the reduced probability of winning, international titles yield much greater expected prize money than domestic titles do."
Although this statement is rational and may even be true in almost all cases. I think it is clear that this is not necessarily the factor which most motivates. The Chinese and Korean youngesters are both in systems in which rank is 'everything'. Their entire day, everyday, is devoted to improving their rank amongst their peers. To ignore the power of social status is a mistake. Look at your own life: your hairstyle, your clothing, the car you drive, who you spend your time with. All this and more will depend in a big way on the social status(rank) associated with them. Why you imagine these people to be any different, I don't know.
"I get the feeling that top Chinese pros and top Korean pros are slightly stronger than top Japanese pros (for pros a "slight" difference in strength makes a huge difference in results). However, I believe that the reason for the difference is not because either country has a superior system or natural talent."
I don't think there is anyone reason...
"My personal theory is that top Chinese pros are stronger because they get to play top Korean pros often in international tournaments (and top Korean pros are stronger because they get to play top Chinese pros often in international tournaments). They simply get to play serious games more often (perhaps twice as often) against top level competition than Japanese pros do."
... but it appears that the current crop of Chinese and Korean Pros are "naturally" more talented. Possibly because the pool from which they choose is larger.