I read the account of her lunch out at one of the Pig restaurants, they're not particularly cheap. The occasion was to celebrate a friend's birthday. I don't think it's unreasonable to want to enjoy a meal without it being interspersed by children's noise. Really it's up to the restaurant to officiate in this respect, I understood they took the part of the parents.
We often would take our children and more latterly grandchildren to Pizza Express which is a pretty child friendly place, but with the expectation that they were to behave in a way that wouldn't impact on other diners and because they regarded it as a treat, they didn't let us down. I think it's up to parents to impress that on children, people pay money to enjoy a meal out and to cause too much noise, running around etc. can and does often ruin it for others. After all it's never too early to learn consideration for others imo.
I don't believe there should be a blanket ban on children, personally we never took ours to a place that I'd consider more conducive to an adult occasion, but I really do think that if parents know their child is likely to cause a ruckus then taking them into an environment where that will impact on other diner's enjoyment is selfish.
In this instance I veer towards Jan Leeming's pov, even though she didn't express that very well.