I can see both sides of the argument, perhaps it's wrong to have an overall ban on children after all they are part of society and eating out can be a good experience for them. It's up to parents to ensure that they don't run riot possibly the care should have stressed that instead. I always tried to instill into mine that if they behaved badly then it would ruin other people's experience and we wouldn't bring them again, that usually worked. We tended to take them to Pizza Express type of places rather than coffee shops. In coffee shops I've seen perfectly behaved children and terrible behaviour, two experiences really stand out, one where two or so youngsters were actually having a race in a Marks and Spencer cafe, albeit it was fairly quiet at the time, but the couple of customers there weren't very happy. The other was in a well known coffee chain, quite busy, two siblings maybe 3 and 4 were running around, one fell over. Normally the staff aren't very pro active in dealing with this sort of thing but in the latter instance one did ask the parents to take the children out as their behaviour was endangering them and the other customers 
I think it's all about the parents and those who maybe have an over inflated sense of entitlement. There was a thread over MN recently. Four or so friends were having a drink/meal in a pub and were using a vacant chair for coats etc. Family come in with a young child and take an adjacent table. One child has toy giraffe, places it on it's own chair, thus leaving the family with one chair short so mother approaches the friends and asks if she can have their "coats" chair, giraffe had to have it's own seat apparently. The party of four refused on the basis that the soft toy could be moved but pointed out if the chair had been required for an actual person they would have given it up. Mother went off huffing and puffing. Most of the posts were of the opinion the mother was bang out of order putting in such a request and I think it illustrated how entitled some parents' are regarding their child/ren.