I have studied Aikido on and off for 25 years, more seriously the last 10 years. Aikido appealed to me in the beginning because it did not require that I accept any concept on insufficient evidence. In my teaching, I refer to "ki" in non-mystical terms, as "enthusiasm" or "vitality" or "intention." None of these captures the full value of "ki" as an organizing principle, but neither do they require a leap of faith. I leave it to individuals to further define the concept from direct experience.
On the topic of organizing principles, the martial aspect of Aikido has been very helpful to me in focusing my practice, but I don't consider it central, nor even required, to get value from training. A woman in her 50s who is near to retirement doesn't need or want to prepare for MMA. But, as a dojo, it is in our interest to make a space for her on the mat, because efforts to optimize her training strengthen the whole community. Aikido captures her imagination and motivates her to come to the dojo. The positive results are verifiable and so long as she is not encouraged to start bar fighting, there is no down side.
An Aikido dojo could function as a rationality dojo. As could a bridge club at the senior center or a trivia night meetup. I think you have to start with a thing that people actually want to do, then build a community around doing that in a way that strengthens rationality. It would be more useful if it was something that irrational people want to do, because they need training the most. Maybe slot machine school.