My Klipsch Cornwalls, with heavy 15" woofers, were made in 1977. That would be 34 years ago.
Shockingly, the voice coils are not rubbing, nor do they need a woofer bra, though some enterprising audio company may take this as a que to begin marketing one.
Many of my friends own even older speakers, some from the 1940s and some with heavier cones than the 15" Klipsch, and interestingly, none seem to be sagging.
File under "urban legends" or "audiophiles have too much time on their hands in the summer."