I don't think so. This is simpler, it's just stating that an optimization problem on a constrained information set must be weakly dominated by the full information set.

Arrow's theorem is a more domain specific and elegant proof regarding political properties that can be simultaneously held.

More like the orthogonality thesis, I think. These different value axes are totally unrelated, and building an algorithm that maximizes one does not necessarily mean that it maximizes the others as well, and this mismatch can have disastrous consequences, a la "The Paperclip Machine"