One reason why middle management loves LLMs probably stems from it being a yes man, no matter what you ask it to do, no matter how stupid, the answer is praising the asker, and just doing it, no matter how bad of an idea it is.
It's not like the pesky workers like me, who will tell you that this is a disaster in the making, that it's a bad idea because of x or y reason, and will suggest something that is simpler and maybe not as fancy as the ask, but something that will be performant and maintainable.
While in the end it ends up being better with the pushback, it's not as nice for their ego. But institutional knowledge and experience are things that are important, and it seems like it's something the management-class is hell bent on eroding.