However, the azan is an audible call to prayer which needs to be disseminated and heard, and the loudspeaker is the most efficient way of doing so. You can't use the same arguments you did against the lectures, because I can come back and say "Yes, but it's a summons and so logically must be aired when necessary".

No I can, because it doesn't need to be disseminated over loudspeakers. As mentioned by others here, thanks to new technology there are plenty of ways to get this so called "call to prayer" to people.

I agree, which is why the azan being aired over loudspeakers should be considered okay. As I said, it's a call and a call needs to be heard. To be heard, a call logically needs to be loud.

No, logic isn't blindly following rules prescribed in what could very well be a work of fiction based on one guy's recollection of his conversations with his invisble friend. Something like this could easily qualify as a public nuisance and therefore should not be disseminated in such a manner.