"It makes the speaker more secure on carpeting and increases the chance you'll have them level as they're not floating on the rather inconsistent weave."

Thanks for clarifying the additional benefits of spikes on carpet. The same reasons also explain how sound is improved with spikes on carpet. The speaker enclosure produce the sound without the interference of the vibration of the box on top of the carpet which could smear the sound. More so, if they are not level.

You are asking me to prove it but it looks like you are also using spikes on carpet maybe for other reasons but you also get the benefit of improved sound.