Comment by AstralStorm

Even with binning, the problem is one of accurate sampling from an unknown probability distribution.

Biased samples produce biased results and this OP correlation coefficient might be sensitive to such an issue.

In one of the projects we were assuming gamma distribution (for speech processing) and sampling that is notoriously hard. Trying to use binned MI produced serious errors, as opposed to Minimim MSE one, even Maximum Likelihood did better (if noisy).