Are Paul and I disagreeing?
Not really.
Again, let's go back to the basics of a cymbal...
It gets struck by a stick (It's impulse response) and it vibrates in response to that impulse... it's surface will exhibit modes as the vibrations travel the surface of the cymbal and yet the cymbal itself will move in an elliptic fashion following the force and direction of the impact.
So far so good right?
The cymbal has to displace air in order for it to be heard, air which has a weight, air which due to its properties will do its damn best to go back and fill the space that was left void.
Air who also acts as a dampener, because it has friction, because work has to be done for the cymbal to displace that air, work which dissipates as heat, heat which is not infinite because neither is the work nor the initial force.
So as you dissipate heat, you have less energy to work, and after each oscillation you'll have less and less energy, until you reach thermal equilibrium... you have no more energy to dissipate, your initial hit, which exerted a work potential on your system has dissipated.
And so far you are in agreement with Thermodynamics.
Your cymbal will return to its original state before the impulse, it might be a long time, it might be a short time, it all depends on the efficiency of heat transfer and the work efficiency.
So far you are in agreement with basic Newtonian physics.
There's no feedback on the system.
But what if you were actually playing against a wall? Wouldn't reflections act as feedback? No, simply because their force contribution would be significantly less than those of the system and they will also diminish with time.
If a butterfly batters its wings in china, do I feel it on my cymbals? Sure, does it change the state of the system? No...
Likewise with a speaker cone, a microphone diaphragm, and even a tuned pipe on an acoustic organ.
And here's where people get their cables crossed.
If I model a speaker, I can simply model its frequency response as the product of two bandpass filters (One high, the tweeter and one low, the woofer), if I take that model and look at its impulse response it will have an infinite impulse response... sure, and that's not contradictory, it's a model.
But if you want a real world extension of your model you need to add losses, non-linear behaviour of the speaker cones, breakup modes on the cone and so on...
It's no longer the product of two band pass filters. It becomes a complex differential non-linear system, whose impulse response is not infinite.
So Paul is right, and I am right, and so far neither of us are contradicting each other.
To the experiment yourself, grab a speaker cone, wire it to a toggle switch and press it, recording the output with a measurement microphone, leave it a long time...
You won't be able to measure below the noise floor of the microphone however, but if you have a spectral interferometer and a couple of lasers handy it makes for a very fun experiment.