On the contrary contrarian, batting order, like the rotation system, is of inestimable importance. But its importance is above all - AESTHETIC ! (It helps to live in Italy to note the importance of aesthetics - country's shaped like a boot, great fashion and design industry, nice leather jackets, pretty people wearing nice clothes, Renaissance art, beautiful architecture - but I digress...).
A catcher batting first is just ugly, even if he is Tim McCarver. Batting Harmon Killebrew ahead of Rod Carew jars the senses.
Willie McCovey - Willie Mays - Jim Ray Hart is bearable, but Mays-McCovey-Hart is much more satisfying. Hart-McCovey-Mays does not work at all.
Batting Johnny Damon fourth is unpleasant, as would be batting Kenny Lofton fifth.
Four man rotations, as even Bill James admits in his one concession to non-sabermetric logic - indeed as he dreams of - are aesthetically the most pleasing - 3-man and 5-man rotations are ugly, though to be sure it is often impossible to achieve four man rotations. But that difficulty is part of what makes them a goal to be achieved, and all the more satisfying when it happens.
Indeed, I will even take a page from my poet friend (?) bagchucker - his love of triples is above all aesthetic. So be it. I think the most beautiful offensive play in baseball is actually a bases-clearing double, but I see his point.
The bible so to speak, on this issue, remains the greatest work ever on sports - C.L.R. James, Beyond A Boundary. For those not able to wade through the chapters mainly about cricket, read the preface, then skip to the two essential chapters: "What Do Men Live By" and "What is Art".
Take, as an example, the great 1975-6 Reds - Rose leading off and then Morgan had a great appeal, though even if reversed it worked, since Morgan was fast as well as having good OBP skills, and Rose was a good number 2. Then, the aesthetic broke down - Bench, Foster, Perez, were all essentially number 4 hitters. Griffey was an excellent number 2 hitter, and perhaps Morgan in the number 3 spot with Bench and then Foster improves the aesthetic appeal. But Perez is a number five hitter or four, not a number 6 hitter. And his skills were too good to drop to 7 which is for low average, good but not great power hitters. No one has found the ideal number 8 hitter, let's admit that, though everyone knows on nearly every team who should bat 9th.
The 1 inning closer has not aesthetic appeal at all. None. Stoppers have appeal, but that position is a lost art - coming in in the 7th to finish the game, or in the 8th. Setup men however still appeal and long relief has a gruffy aesthetic of its own. Different kind of bench players for different roles - pinch hitters, pinch runners, utility infielders etc. all have their fashion.
But Bill James points out about Earl Weaver that after his 1969-71 great Orioles team faded, Weaver went with four men rotations whenever possible arguing that it is easier to find four good pitchers than five, and realized the great truth (now forgotten) of the DH: it EXPANDED his bench, since he no longer had to pinch-hit for pitchers (the DH aesthetically is as awful as a 1970s midwestern stadium, but once it was there he made the most of it): it freed him to have three great infielders fielding wise, and a bench with three others and three OF-1B with power to pinch-hit for them. So he could have them play 6 innings backing up the starter, pinch-hit and then put in the bench IFs.
What he never had on his roster, and it is clear that aesthetics as well as utilitarianism were at stake even for Weaver, were players with 500 AB, a .260 average, 10 home runs a year, limited speed, weak defense. These were no aesthetic appeal players all around and also served no purpose. Form follows function as Frank Lloyd Wright always said (or was it Lukacs?) but form is still important.