No one is saying that they desire a private British Club
I'll say it. It would be nice. Keep the women out too!

Give them a Ladies lounge. I'm sure most women would prefer that anyways.
but I would say that the Club is more intended to be a place for business people and adults to relax during and after a busy day - and clearly intended to be a private quiet elegant haven away from the bustle and noise of the rest of the hotel than it is to be a place for children
I'm sure that kids are not the intention of the design, at least at non-Disney hotels. But the *result* of the design is that they are great for kids.