Existing infrastructure is emitting CO₂. The stuff we replace it with won't. The gas pipes that are shut off will no longer leak methane.
The next century will be dominated by how we deal with the last century's monumental carbon emissions. We went from 300 to 400 ppm by burning immense amounts of fossil fuels. To go from 400 back to 300 will take a bit of effort. No single policy—in isolation—will "reverse climate change". But all of them will.
CH4 is the larger concern with natural gas
This paper explains it:
It will take a generation to upgrade every kitchen. These sort of "start the incremental change" ordinances need to happen at some point. Might as well start now.
Burning gas at a power plant to generate electricity is still much more efficient than burning gas at home generate heat for cooking.
Or: When you purchase that EV, what are you doing with your previous car?
2 different perspectives, both require new stock to enter the market. That new stock should be EV.
Even charging an EV from a gas-fired power plant is still more efficient than burning gasoline in an ICE. Yes, even with transmission losses and charging losses. Burning gasoline in a small engine is wildly inefficient compared to utility-scale turbines burning natural gas. Hybrids have done a fantastic job in basically doubling this efficiency, but they're still no match for grid energy.
My grid averages about 233kg CO₂ per MWh delivered.
If I had an EV, and I charged it with 3,600kWh each year (12k miles), my annual CO₂ emissions would be around 900kg. Half of this is from gas plants. If I toss some panels on my roof, then the yearly emissions way down.
A new Prius driving the same amount is around 2,100kg.
So the argument comes down to the embodied carbon in the supply chain. The carbon released for EV manufacturing is about double that for a gas-only car. (I don't know where hybrids land on this, probably closer to gas than EV with their small batteries?)
But the operational emissions dwarf the manufacturing and disposal emissions. Cars last a really long time these days.
There are some regions (coal) where an EV will tie with a hybrid for net emissions. That's the worst case, a tie. But only one of those will automatically take advantage of grid improvements, more solar, etc.