Hmm, this is interesting, but I have few doubts about it. First, Metane is worst gas to come by. Its super greenhouse gas. Second, everyone screems about carbon neutral, but do those people understand carbon cycle on this planet? Its essential for plants. Less CO2 in atmosphere, plants growth is slower. If you start to compete with plants for it, it might have unforseen consequences.
I hope someone will put some research on it. This is usual human aproach. Lets fix one thing, worry about consequences later.
We've spend the last 2 centuries burning fossil fuels from the ground, significantly increasing the atmospheric CO2 levels. Capturing some of it back won't make a difference for plants.
Also, when you burn methane, you release CO2 again. So it's not like there's a finite amount of CO2 to pump from the atmosphere, it will renew itself.
I hope someone will put some research on it. This is usual human aproach. Lets fix one thing, worry about consequences later.