The amplifier will be class-D, the inductors are simply filtering on the outputs - so wouldn't cause crackling - it's almost certainly not the problem, and isn't something I would have even considered.
I would also suspect the inductor is simply a different type to the ones around it, which is why it looks different, and the 'tops' of the other ones aren't shields anyway. You might like to identify which channel that inductor is associated with, if it even is on one channel only, if it's not the crackling one then it's even more obviously not that.
Back when I was fixing such things most usual causes were dry joints, or intermittent relay contacts - for those systems that have speaker protection.