I love a lot of the insights in here.
I do think the fact that humans are so dependent on each other does mean that the social benefits of logical consistency are often of the utmost importance though. And I think there absolutely should be a social cost for communicating in a logically inconsistent way. I actually wrote an article* called '4 things all good citizens believe implicitly' in which the fourth belief is 'Logic builds trust', which is essentially making this point.
Although I agree with you that we shouldn't "force" people to prematurely rationalize emotions or behaviors that they may not understand well enough to articulate. That's essentially a recipe for getting bad data.
I would also say that logic does have value for the individual too. Math and science, for example, can help you build a house or machine, whether you need to communicate with other people about it or not. It seems like logical consistency basically helps us interface with anything that is outside ourself.
* https://medium.com/@nebulasaurus/4-things-all-good-citizens-believe-implicitly-dd37c4dbef6#b48e