Why not, though?

On a serious note: that's exactly what we're doing with lighters. At least some of them use piezo elements and not the sparkly wheel thingy to ignite the gas. And it's real fun to zap yourself with it.

Give buskers the acoustic guitar with a link to the grid and every time they play they’ll generate a ton of electricity (in relative terms…)

Electro-Acoustic guitars use piezos to pick up the audio if you didn’t know

Wait a minute, what IF

Even if we used piezo, the movement of the hammer would still have to come from some power source, which would still be the same sources like moving steam, water, or wind.

piezoelectricity is just simple electric motor