the snare is not the beat its the "drive". the bass drum is the beat. the bass guitar is the bottom end. the rhythm guitar and/or keyboard is the rhythm. the lead giutar is the voice instrument. the snare doesnt have to be a little louder in the mix but its my prference along with other people. it should be just loud enough to notice that it a little louder. the drummer should be hitting it hard but not so hard that it dents the heads. i'v ben drumming since 1970.
Sure you have been playing the same style since 1970 but not all music fits into that narrow perspective so it defeats the purpose of helping an artist create if you go into the show with preconceived conceptions of how it "should" be.
As you said in your post above sometimes the snare is In front of the beat. Sometimes it is on the beat and sometimes behind. As a mixer it is not my job to determine where it should be but if the artist wants my help I will make sure there is room for it where they want it.
To paraphrase a departed member of the boards the way to become a really good mixer is to listen to a wide variety of music and to gain experience doing a wide variety of shows. Personally I don't think anyones skills mixing rock will be hurt by learning to mix a good jazz drummer.