If it increases the probability of winning like that highly successful irrational person, it's still worth doing. I mean, if an irrational person has a 20% chance of becoming highly successful, and a rationality training could increase it to 40%, then I would prefer to take that rationality training, even if the rewards for the "winners" in both categories are the same.

The idea here is that even if "rationality training" (or even general intelligence) gives people an overall advantage, there is a possibility that there are systematic disadvantages in some areas which arise when a person repeatedly uses reason to override emotion and instinct.

Relying on reason and suppressing emotion and instinct is a cultural value, especially for people who call themselves "rationalists". We need to be aware of the pitfalls of doing that too much, because instrumentally speaking instinct and emotion do play a part in "computing" rational behavior.