Social reasons it would never work. I hate to mention anything race related online but simple truth is America has complicated history and African Americans are 30% more likely to be obese than White Americans and also earn approximately 60% of income that whites earn. A fat tax, especially one that properly allocated the cost burden to the individual, would erode race relations.

fwiw the “tax” in Japan is not paid by the individual, and generally taxing the behavior via e.g sugar taxes rather than the outcome has worked better without much public outcry after the fact