But I think you're wrong to think that gas is "critical" to any of the things you've listed. "Currently used" ... yes. "Not replaceable by electricity" ... no (unlike, e.g. air travel).
Electrical heat using heat pumps is cheaper than in-situ heating with any fossil fuel because (a) the base price per unit of energy is (or certainly can be) lower (b) the coefficient of performance is higher.
There are obviously costs to changing heating systems. But that doesn't mean that a gas heating system cannot be replaced by an electrical one.