I taught kindergarten for about 7 years and whenever I told people my job, I got one of two responses "Oh, that's so cute!" (ha!) or "You must be a saint" (I am! LOL)
BUT - whenever I talked to people who said they taught middle school, I always gave something along the lines of "You must be a saint" and then when that person found out I taught kinder, they had the same response!
I think it all depends on the person! Some people do really well teaching young children and others do really well teaching older students.
If you look at your list, all teachers have to teach kids to take tests/care about results, shy kids, loud kids, respect, etc. ALL teachers are responsible for those things, J. in different ways. I might tell you that I prefer the younger kids because they are less likely to talk back (even though they still do, it was easier for M. to reprimand a 5 year old telling M. to F*uck Off - yes it happened - than a 13 year old!).
I don't think different grade teachers should be paid differently. They all work hard in there own ways.
With all of that said, my mom taught children early childhood through adults in various types of settings and she ALWAYS said, the younger they are, they more work they are. But then when she taught alternative HS, she used a lot of the same discipline/behavior incentives she used with her little kiddos. She said it was very similar to teaching early childhood, they still had behaviors and sassy mouths, they were J. taller :-) Still needed respect, love, encouragement, and someone to believe in them :-)