Methane is far more potent as a greenhouse gas

And the best case scenario is burning it somehow in which case it just has a CO2 byproduct

Weirdly, burning methane gives you both energy and decreases its carbon footprint by ~30x (the mole ratio is 1:1).

Methane decaying just means the atmospheric concentration doesn't increase as fast. But if you emit more than the previous year then levels will go up. And indeed, levels are currently 3 times what they were from pre-industrial levels [0].

The EPA says its Global Warming Potential over 100 years is 28-36 times CO2 [1]. 100 years sounds like a very relevant time period to me.

[0] https://en.wikipedia.org/wiki/Atmospheric_methane#Patterns_o...

[1] https://www.epa.gov/ghgemissions/understanding-global-warmin...

I hadn't heard that methane didn't last too long in the atmosphere before. What happens to it?

The UV part of sunlight breaks it down into CO2 and water. And before you get too worried about the CO2, that's from "current" carbon in the environment (the grass that the cows ate) not fossilized carbon. So it's not a net addition of carbon to the atmosphere.

The carbon is coming from the methane, though. I don't have a degree in chemistry, but the carbon from the grass doesn't end up in the atmosphere naturally, does it?