I doubt that there’s any correlation between shoe and MBTI type beyond the more general motivations for wearing a shoe pair, like for instance aesthetic interest versus strictly practical reasoning, though I suppose your Rational shoe type hypothesis does match up with me. I generally don’t care about how my shoes look as long as they’re practical for the situation with the minor exception of some color coordination, in which case I prefer relatively plain colors such as black, gray, or brown. I’ll wear a pair of tennis shoes for a few years and change them when they begin to fall apart; I after all own them so that it’ll be easier to run and perform other athletic activities so they’d be worthless if the soles went missing. I do wear boots in the snow, however, and along with my tennis and formal shoes they comprise the only three shoe pairs I own at any particular time. By the way, while I'm interested in exotic shoes such as moccasins and Japanese geta (Edo Era wooden sandals) I don't tend to wear them for the practical reasons mentioned before.
I wear functional shoes (I would never buy a pair of white shoes that would get wet or dirty easily, for example) but they have to look stylish too. I wear mostly casual sport shoes like my red Keen Newport sandals, Keen Sydney shoes and Merrell moccasins.