I don’t understand how any of those points would help at all. Number 1 is irrelevant and number 2 is easily handled.
“Oh, neighbor didn’r hear a gunshot? Well let’s put down the guns and knock on the door nicely instead”. Come on now.
And why not? In the same situation in Europe, this is what would happen. Regular cops would confirm the situation first. And it works. Units similar to the SWAT do exist, but I've never heard of them being dispatched directly after an anymous call.
"if all you have is a hammer, everything looks like a nail...", and well, the SWAT is pretty much a hammer in this kind of situation.
I'd personally be shocked if it were any difficult to get a hold of the GIGN, the RAID, the DGSE, the GCHQ or the UK SWAT when necessary.