No, you can't expect kids to learn how to act in society if they're prevented from existing in society. Besides most pub style places are already adults only after a certain time.
Imo there should be child free areas, yes. Or at least a minimum age to enter a “child free zone” like 5 or 6 or something. Not everyone wants kids or likes kids, and it’s not fair to those people to hear kids screaming or making a ruckus or whatever in a location that can reasonably be assumed to be “adults only”.
So that parents can only go out for a meal if they also have another $100+ to spend on a babysitter? No, my 2 year old is coming with me and getting $6 chicken nuggets.