What's the benefit of ammonia vs. turning hydrogen into methane via carbon capture?

Carbon capture is hard, nitrogen is truly abundant. That is unless you happen to have a source of highly concentrated CO2 at hand. Which is certainly true now, but won't be in the endgame. Methane (or something with an even lower H-per-C) will surely be part of the picture, but it can't be the mainstay. I'd expect hydrolizer capacity to cluster around storage opportunities (like salt caverns) within convenient grid range from energy sources, large ammonia plants to continually work from that hydrogen buffer and higher-value H2 consumers to opportunistically tap into the same buffer whenever their "other ingredient" is available. That "other" could be metal ores, iron oxide returning from an oxidization energy cycle or CO2 from biomass burning or waste incineration. But there's always hydrogen as a first step, and the (centralized within grid range) hydrogen storage as the buffer that solves the dispatchability problem.

Fun observation: If some of the hydrocarbons created this way make it into plastics that isn't passed back into incineration (or a better form of recycling) you'll have true carbon-capture for the fraction of the carbon that came from biomass. Without we trying.

Thanks for the detailed reply

This. Is there even one power2anythingelse that does not have hydrogen as its first step? Hydrogen storage will be important, as the input queue for whatever step comes next so that only the hydrolysis capacity has to be scaled for being able to take in supply peaks and idling the rest of the day/week/year. But hydrogen storage won't be involved at all anywhere in transportation or distribution of energy (with a few possible exceptions in large very high energy density requirement applications, I wouldn't completely rule out hydrogen aircraft being less infeasible than e-fuel powered aviation at scale)