Don’t confuse purified water with filtered water. Purified water (often reverse osmosis or deionized) removes over 99% of contaminants—close to distilled, but less energy-intensive. Filtered water (like from a Brita) only removes taste and chlorine, leaving most minerals intact.
So, is filtered water better than tap? Marginally. A carbon filter won’t stop the white dust. You’d need a demineralization filter or a pitcher that specifically targets calcium and magnesium. If you’re lazy (same), just buy distilled.