I think you have summed it up well.
In essence with noisy adults, the adults can be held directly responsible for their own behaviour and there are some options open to other adults. With kids, the attitude is the opposite and that it is kids being kids and the onus is transferred onto everyone else to simply have to compromise their desire for peace to the childrens needs to be kids and be noisy. This is made worst now because over time parenting has become less concerned about the discomfort of others. There is no other solution to that conundrum. The conclusion therefore of allowing adults wanting better odds of a more serene adult environment is to allow that occaisional sanctuary for which you pay a premium. I think that seems reasonable to most reasonable people. The idea that kids should be allowed anywhere and everywhere isn't a human rights freedom issue.
I think those that make the arguments that there are other and equal forms of annoyance are obviously correct but it simply fails to confront this one.
^
Agreed. If you pay the price for a room that includes club access, or get it for "free" due to your status (in which case you're still paying, just with loyalty), you should be able to expect that you can go in, and enjoy a quiet, relaxing setting away from the hotel proper. And honestly, I'd be just as upset if it was a businessman or etc causing the commotion. You should be able to go and relax and lounge, not deal with whiny brats - whether the brat is a spoiled businessman or a spoiled child is irrelevant.
And it's unfair to tell the kid "hey, I know you just want to play, and I know there's more than likely a pool just downstairs you'd love to be swimming in, but right now I want you to sit here quietly so as to not disturb other guests."
Let the kid be a kid... somewhere else.