I really don't want to hear a slippery-slope argument. They do nothing for debates. This isn't a slope issue - it's a solution to a problem with well defined boundaries. You can't simply force customers with disruptive children to leave because then you have issues with securing payment. How do you define disruptive anyway? Having a defined age is a practical means of getting rid of disruptive children. Most parents aren't going to reasonably say "well my kid still cries and screams, but just turned 3... so he should be ok."
However, the underlying problem: Parents who take their children to restaurants (or anywhere public) should be respectful of their surroundings. If you're using public transit, or eating out, make sure your kids aren't causing trouble. If you can't control them, the you leave. Your kids are your own responsibility, and just as I leave a place when I feel uncontrollably enraged, you have an obligation to leave when you can't control your children, and they're disturbing others. If everyone did this, there would be no need for these kind of rules.
I can't believe someone didn't put in a rule like this earlier.
The biggest drawback to first class is that you're much less likely to get nice seatmates.
Not to mention: This isn't a ban on children, merely children under 6.
I see your comparison more in a quite different light which I often encounter; if you let kids in, why not dogs? My dogs don't bark, whine, poop, pee on the floor, don't run around, don't break things, don't bite things, don't beg for food (or icecream) really loudly; something which I have seen young children all do (yep including the barking, seriously) in public places, including airlines and restaurants.
It is perfectly legal and acceptable to throw someone out if they or their party are being disruptive.
Banning them simply on some artificial criteria is a bad idea.
You would have to actually enforce the rule, and that would be ugly, but it would have been way, way less ugly than what's happening right now. And it would have been just as good for publicity, if you advertised it.
I'd just hope that the staff makes the policy very clear because this is definitely outside the cultural norm. I'd be REALLY mad if I made reservations for something like a nice Father's Day brunch, showed up and was told that I could eat but my daughter would have to wait outside.