However, "imamat" by itself is a generic term, so it's not clear why it should be controlled by a single organization that happens to have it in the name.

Given that this discussion was started by someone mentioning only these 3 related things, I'd guess that the motivation might a negative one.

Aren't there tons of generic terms gTLD controlled by a single organizations now?

I've just learned here that .man is owned/controlled by the MAN group

edit: source: https://icannwiki.org/.man

also: walmart applied for .george https://icannwiki.org/.george