Burning natural gas instead of coal should result in about half as much carbon emissions theoretically, although methane leaks will narrow the advantage.

Absolutely. Gas is a lot less problematic than coal.

But my point is that it fills (in China) a very similar role for the electric grid and countries don't get to choose what fossils are in their soil.

The US using relatively more gas than coal is not any kind of laudable achievement, it's simply whats cheaply available.

Norway does not get any credit in my book for being full renewable either (because they have "free" hydro power literally everywhere).