I'm as density-friendly as it comes, but I think that we'd be much better off at maximum 20,000/sq km or so.
(That's not a magic number - that's about the density of the city of Paris, ignoring inner ring and outer ring. That's average across Paris, mind you, not some absolute maximum.)
Oakland is 3,000ish per sq km, for reference. Now, I'd prefer that we don't have to live in the 400 sq ft/40 sq meters kind of options that are older Parisian apartments, and I think that proper sound insulation is ground stakes (which current 5 over 1s in America don't do a great job with) but I think we can make the argument of more density without pushing for the extreme argument here.