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I've seen this said before (notably, Larry Summers took a lot of heat for saying it) and it seems like the kind of thing that might well be true, but I've never seen the actual numbers. Have you actually done the calculations?
I got the calculations from La Griffe, linked by gwern in a sibling comment. (For completeness, [1], [2], [3].) I have a vague recollection of checking them myself at some point.