Bingo. I do not. With one important caveat. And we'll get to that. Let's consider first Goldschmidt's splits for this season just so everyone is working from the same deck of cards:
Batting 2 -- .266/.359/.439, .798 OPS
Batting 3 -- .226/.294/.396, .690 OPS
Batting 4 -- .318/.366/..647, 1.063 OPS
He has a grand total of 17 games at cleanup this season and three times as many plate appearances at the other two spots this season than he does cleanup. So, let's broaden the scope a little bit, and here are his splits from the previous three seasons:
Batting 2 -- .349/.432/.672, 1.104
Batting 3 -- .291/.405/.508, .913
Batting 4 -- .281/.374/.519, .893
Well, the larger data pool tells the opposite story. Stats are funky that way and we can all make them dance and sing the tune that we want depending on how we carve them, and that's why context is so key. Enter the caveat. One of the things that does play to your implied argument that Goldschmidt bats better at cleanup is simply that with more chances to get people on base in front of him, the more people there will be on in front of him, and that will change how he's pitched. Great protection starts by putting people on base in front of a fear hitter so there's no where to go with him except into the strike zone. Goldschmidt, as we've discussed and detailed often in here, has not had that many at-bats with runners on. Not as many as a hitter like him should. That's going to change how he's pitched, and you can see that when he was in the cleanup spot and batting more often with a runner on base or in scoring position it helped him.
The tradeoff would be getting him far fewer at-bats to be the guy on base for the people behind him. That's what you have to figure out. One solution: Put better OBP players ahead of him. Which the Cardinals are now doing.