This is very similar to an Aeolian Harp, also known as a wind harp. https://en.wikipedia.org/wiki/Aeolian_harp https://www.youtube.com/watch?v=CtzSm76ppS4 They are pretty cool art installations. The Golden Gate bridge may now be the largest such installation ever built!
Yes, it cannot be a 24/7 thing, the harp/bridge is too loud. Also, putting resonances into a suspension bridge is likely to be unsafe.
That said, like the chiming of church bells in a village, it may be used selectively. I can imagine some Burners quickly putting up an adjustable mechanism to have the bridge sing/chime.
Something that can point into the wind correctly (to some degree) and then be readjusted to turn off. Possibly to make more than just one note, like a carillon of bells in a bell tower.
Maybe at the tops of the hour it can turn on/off, like a church bell, to signal the time. Or on special occasions like New Years Eve, the 4th of July, etc. Or for swearings-in of a mayor's term, etc. Heck, even as a warning system for earthquakes.
Having that loud of an instrument, powered by the wind, and then controlled by a few hundred actuators or a bridge-worker/bell-ringer moving steel beams in and out, it's just too good of an idea.
If something like that could be made to work, on such an iconic bridge, well, that's a whole new industry. People have done 'love locks' for years now, chiming bridges would be a great idea too.