Wouldn't that only be relevant if the old ones weren't also machine-washed? Also, what % of people in developed countries are handwashing their underpants? The only semi-widespread handwashing I'm aware of in developed nations are for wool sweaters and sometimes women's bras.
Line drying was not common in the 1990s (in the US) when the claim is underwear lasted. Washing machines have switch to low water use versions, so that might be a factor (I doubt it, but it the only other thing I can think of)
Line-drying is very different from "hand-washing".
I "line-dry" (drying rack) a lot of my clothes (pretty much all my dress pants, dress shirts, anything that I don't want shrinking in a hot dryer). But I don't use a bucket or tub to handwash and handwring my clothes; I still machine-wash on delicate with cold water even if I line dry. I've never met anyone who hand washes, in any country (though I know it's popular in many less-developed nations, I haven't met anyone who does).
I have occasionally handwashed very expensive wool sweaters, but I prefer dry-cleaning them, not only because of the labor but also because if I let them soak even just a little too long the wool fibers start separating and permanently changes the sweater.