Costs aside, wouldn't replacing carbon emissions with methane be drastically worse? Doing a casual search says that methane is 2000-3000% more potent as a GHG.
Pure methane is a bunch of molecules with just one carbon, which simplifies things a bit vs. a cracked and heterogeneous mix of longer chain (10+) molecules.
You can incompletely combust a 10-carbon molecule and wind up with other hydrocarbons but if you burn up CH4, you're definitely just getting one CO2.