Not sure that would play the same in US though.

Black population in the US is still concentrated in neighborhoods formed by overt racism and segregation and same neighborhoods tend to be food desert where no healthy or even fresh options exists. Even if we taxed just the bad food, the lack of options and mobility that higher income might provide, basically means it’s something that would be seen as targeted. Not to mention, people will draw the most racist perception no matter how carefully you crafted the tax because race relations are always unfortunately weak and these correlations are being forced/drawn.