"For half of the tap water sources we examined, adults may fulfill between 8% and 16% of their Ca2+ DRI and between 6% and 31% of their Mg2+ DRI by drinking 2 liters per day." from https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1495189/
And another paper on calcium: "On an average basis this would represent 5% to 10% of the usual daily intake or approximately 6.5% of the adult RDA." from https://www.ncbi.nlm.nih.gov/books/NBK216589/
The calcium seems negligible. Magnesium is a top nutrient deficiency in Western diets, so could be somewhat negative, but because of that I (and probably you) should be supplementing magnesium anyway. Sodium is obviously found abundantly in western diets.
So based on that, I don't think re-mineralizing's tiny benefits are worth the potential risk of re-adding negative contaminants somehow.
But it does hint toward a potential linkage, which is our food system.
The areas you are thinking about are also: food deserts, low-income, and low education levels. All of which are stronger predictors of obesity.