It seems CC plants are 45-57% efficient, so let’s go with 50%. A gas furnace is from 80% to 95% depending how old it is.

The heat pump would need to be roughly 2x efficiency to break even. They can be 3x or higher (since they move heat around rather than generating it.) Your statement surprisingly checks out.

So obviously it makes zero sense to use electricity to create methane to then burn for heat. Reality is messy though, sometimes we do things inefficiently because there are other constraints. Being unable to afford to convert to a heat pump system, or being in a climate where it won’t work well.

Maybe you have radiators that require higher temps than can be efficiently produced by heat pumps. Maybe you live in a place where the air gets too cold for air source heat pumps to be cost effective. Maybe you want to install ground source, but you live in a city and don't have a big enough yard. Maybe you have a big enough yard but local geological conditions aren't conducive to digging deep enough.

Not to mention all the people who just don't want to bother switching, or who don't have the money to switch, or prefer the reliability of the natural gas over the electrical grid, or...etc.

Or just look at the culture wars that are already starting over gas stoves, when nobody has even been required to get rid of their existing gas stove, and people are just talking about changing the rules for new construction.

There are just so many edge cases where it's hard to get people to switch off natural gas. If we can make green methane, all those problems are simultaneously solved with zero disruption to anyone's homes/lifestyles/etc.