I mean your argument is sound enough in that a household's CO2 emissions are trivial compared to big industry or global ecosystem collapse, but that's not the only argument.
Europe found itself in a huge conundrum last year when Russia cut off the gas supply, highlighting our dependency on cheap Russian gas. It meant households went cold and lost their primary means of hot water and cooking - not so much because there was no gas, but because it was unaffordable.
But in my neck of the woods, removing dependency on gas had been ongoing for a while already for various motivations. One reason to do more with electricity, for example, is because people have cheap solar panels on their roofs now, using that to heat their house is (seems?) more self-reliant, cheaper, and less environmentally impactful in the long run.
And sure, one house won't make a difference, neither will a thousand. But it'll start to make an impact at scale.
There is no one fix for climate change, it will take tens of thousands of small changes and legislation over the span of decades.