I believe the effects are more related to performance than structural integrity. Your fins are subjected to forces much more powerful under normal surfing conditions than from humming.
" I've grown attached to the hum as part of the board. Is a fin hum destructive for the fins or fin plugs?"
Back in 1997 I snapped my fun board...my only board at the time....
I bought a 7'6" Bear Speed Egg off the rack at the LongBoard Grotto...Great board!!!! In waves taller than me or in powerfull backside waves the board sings...it does not hum...it's a high pitched noise.
I tried sanding the fins.....they're glass ons...she sings!
That board has been through hell and was my test board when I learned how to fix boards. Today the board is heavy and ugly and next in line for a refurb....
Last summer there was a big south swell and I grabbed the Bear....Two great sessions on an old friend....She sings....
Singing is usually a leading edge defect, near the base. After I fixed a glass-on on my gun, the board would sing only on lefts. It was more a whistle than a sing though, and it would loud enough for everyone around to hear.
Humming or singing is a resonance that will vibrate the fin in frequency with the hum or sing. It may or may not relate to long-term structural problems depending on how the fin is mounted. If it were a glass-on and the sound was loud I would fix it.
Thanks for the feedback. As much as I dont want to mess with the board's mojo - I don't want to irk the fish and dolphins. I'm going to try fine-tuning the fins and try other trailing fins.