Though your comment has a problem. It isn't carbon that is the problem, it is carbon in the air. If we did 100% CO2 extraction from coal fire plants they wouldn't be a real climate issue (overly simplified). Similarly we can't consider sewage as a carbon 0 cycle because eating turns a solid carbon source (food) into a gas. Carbon is fine, carbon in the air is not fine. Sewage is only neutral in the respect that we've already converted it to a gas (unless we accelerate this process, which is typically done) but doesn't account for the conversion process that happens.
It's very good to analyze specific flows, but at the end of day, greenhouse gases (appropriately weighted) in the air are a fungible liability, and taking some specific process and sanctifying it's net greenhouse gas emissions in isolation is silly.
It might be more thermodynamically favorable to use the gas as input to a carbon capture process. Even if that is the case, bootstrapping a market for biogas will lower the cost of biogas. In turn, that will lower the cost of biogas-based carbon sequestration.
Like I said in a sibling post, the big advantage is that biogas is Net 0 carbon wise as you’re reusing carbon already in the carbon cycle
I think enkid's point is agreeing with you: might as well burn that sewage CH4 for energy-- you end up with the same CO2 in the end and less CH4 in the atmosphere in the short term.
