I don't think it does at all.

Burning methane has positive effects on global warming since methane is way way waaaaaaay worse than CO2. Taking care of landfills that are largely untouched, just spewing methane is a good thing. If Bitcoin ends up having a net-negative effect on global warming, how is that a bad thing?

You're assuming that all energy sources are well-connected to a grid that can handle the electricity that is generated, that's not the case at all. You can't "use that same energy for something else currently on carbon-based sources" without major infrastructure costs.