Thanks to you all for taking the time to respond. I learned something!

Initially I thought the wing oscillation rate had something to do with
flutter prevention or attachment integrity. When I was being taught how
to preflight the instructor told me he once found a wing that wasn't
properly attached by shaking a tip.

If wing frequency was being used for wing structural integrity testing
years ago, I'm glad to hear that it's been abandoned! Flaws that can
cause structural failure are much too small to affect a fundamental
resonant frequency.

I can believe that looking for odd ripples or bulges on the wing
surfaces during shaking could be useful indicators of problems, though,
so I, too, will keep it as part of my preflight. I won't bother to
measure the frequency, though.

-John