I mean cities do not work because "what if everybody decides to leave at the same time -and I mean everybody".

"What if its really hot and everybody turns on their aircon at the same time"

Gas heating is inefficient when compared to heat pumps and gas stoves are extremely inefficient when compared to say an induction stove. It simply will not make sense to install them very soon. A heat-pump is really just an air-conditioner with very few extra bits stuck on so houses might have everything in place already. And the grid isn't collapsing because of that.

As for the ban - there might be market forces at play that would make gas real cheap for a time - this would lead to an inclusion in practically all new buildings. But it fairly certain that after that gas will get expensive and supplying it at the individual building level might get less reliable. This will cause a liability because the state will probably be called to fiance the mitigation of that.

Actually I think this will happen regardless. So the ban is simply a way to prevent it getting more costly than it already will be.