Yes...the temperaments came first and happen to correlate with SJ, SP, NF, NT. It's just one way to group the types (why group at all? Because "beginners" can't keep all 16 types distinct. And, for many applications, the groupings are useful)
I personally find the temperaments least useful in the real world of working with teams, teachers, students, leaders, etc. IF we're actually using the MBTI, because of the confusion/contradiction/seeming illogic that started this thread. If you just use a temperament indicator and delve no further then there are merits to the grouping...
The attitude pairs IJ, IP, EP, EJ have a lot to do with our outer appearance/needs--office or classroom environments, workstyle, etc.
The last two letters TJ TP FJ FP correlate with our approach to conflict resolution
The quadrants--ES, EN< IS, IN have been shown to correlate with approach to change and approach to learning
The function pairs--ST, SF, NF, NT--show patterns of career selection, communication styles