A perfect Electrolysis reaction takes about 39kwh to produce 1kg of hydrogen that if burned at 100% efficiency would yield 33kwh of power. More realistically it takes 50-60kwh to produce 1kg that is burned to produce ~25kwh of usable energy.

I'm not too sure about converting hydrogen to methane but that will have energy overhead as well, and then you have to deal with the fact that 6% of natural gas production today is leaked into the air, which both further hurts the efficiency of synthesizing it and also has a significant climate impact.

I think it willl almost always be cheaper to just provide electricity directly except in cases where energy density is far more important than efficiency, which is not the case for stationary homes.

Something like 90% of hydrogen is produced from methane and coal, so there clearly are reasons. Most likely cost effectiveness.

Add carbon dioxide to the hydrogen, and you get methane that you can transport through existing gas pipelines

Well sure, since those pipes are already transporting methane. I dont think requiring each home to have its own methane pyrolysis infrastructure is particularly practical or efficient either.