I’ve just read up on Ti and Te in a book by Jung and I see no difference in my interpretation. Ti is theory, ideas, Te is external facts and problem solving. Ti is only called subjective because ideas and theories are formulated internally. The difference is not like subjective and objective facts. Dare I say Ti is purer because as Jung says Te may become tyrants lol, just as I said about Putin.And therein lies your fundamental error and source of misunderstanding. One cannot understand cognitive functions by attempting to distill their essences from MBTI. Go to the source, and read what Jung actually wrote.
From that, one can come to appreciate the history of typological theory as per Myers, Beebe, Berens, and Thompson.
You are putting the cart before the horse, and reaching some conclusions which have no merit.
Maybe you need to reread Jung?