In humans I think a trivial amount of carbon intake is converted to methane. Ruminant livestock supposedly produce a lot more. I am not sure why methanotrophs in the rumen do not gobble it all up.
The idea of reducing methane production is interesting because of the below linked in which methane production is tied to weight gain. Either 1:methane has pharmacologic effects itself; not impossible given the small size of the molecule and fat solubility. 2: the presence of methanogens somehow augments metabolism and caloric benefit from food. 3: an absence of methanotrophs augments metabolism.
Methanogens have been shown to affect caloric harvest by increasing
the capacity of polysaccharide-eating bacteria to digest
polyfructose-containing glycans, which leads to increased weight gain
in mice.14 Further, previous studies by our group have demonstrated
that methane gas slows proximal small intestinal transit by 59% in an
in vivo model.15 This slowing of proximal small intestinal transit may
contribute to increased weight gain by increasing the total gut
microbiome load or the amount of time during which energy is harvested
from meals. Given the associations between methanogens and weight gain
in animal models, coupled with the finding of an association between
methane and delayed transit, this study hypothesized that human
subjects with increased concentrations of methane on breath testing
might exhibit increased levels of obesity compared to individuals
without elevated methane concentrations.
One would conclude from this that if you wanted to optimize caloric benefit from food you should increase or facilitate methane production. That is not ideal for first worlders humans who suffer from obesity but would be hugely useful for pig farming, where an additional 5% of weight gain for the same feed mass is pure profit.