Copenhagen sort of agrees with observation by introducing non-locality, which disagrees with observation of locality from other observations, which means Copenhagen disagrees with observation.

>But just because it is an additional postulate it does not per se make many worlds the better theory.

The postulate of collapse contradicts the postulate of Schrodinger equation and makes the system of postulates contradictory. By removing the contradiction MWI is strictly better, this in turn also removes non-locality and achieves a strictly better agreement with observation, like special theory of relativity.