Why Vegito chose to use kaioken and not super saiyan blue evolution to increase his power?
There isn't any particular reason, however, the only thing which makes logical sense is the fact that:SSBE was designed to be a Vegeta exclusive form similar to Ultra Instinct which as of now seems to be a Goku exclusive form or even SSJ3 which as of now is only a Goku exclusive form.We haven't witnessed a Goku+Vegeta fusion utilizing the SSJ3 form.Kaioken is a technique and similar to instant transmission which the fusions are capable of using. So it would make more sense for them to use techniques instead of a character exclusive form.Based on my previous point, it would be also interesting to note that based on the nature of Kaioken used with Super Saiyan Blue, ideally, it should be stackable even on top of SSBE as the form is simply an evolved state of Super Saiyan Blue. Which only leads to the conclusion that the fusion was utilizing Kaioken simply as a technique during the course of the fight.