I've wondered that too. I don't have an answer, but maybe they are above some empty areas. Maybe it just can run downhill to the treatment plant. I'd think it would have to be pumped up somehow though.
Uptown is high ground, not as high as the Quarter, so gravity takes it to the river or the lake. Don't recall any canals left uptown.
Descendants of early settlers are not necessarily rich. My family first arrived in the area in 1711.