Dissipates more quickly than what? Optimally, the cows would simply release carbon in the form of carbon dioxide rather than methane, since then you simply have a sustainable cycle:
Carbon dioxide is in the air. The carbon dioxide turns into grass. Some of the grass is used as an energy source by the cow, releasing the carbon dioxide back into the air. Some of the grass is used to make up the body mass of the cow, which is then used as an energy source by humans, releasing the carbon dioxide back into the air.
The point is that the carbon dioxide always ends up back where it started, so there's nothing inherently unsustainable. It's equivalent to growing a tree and then burning it (releasing carbon dioxide) to make use of the stored energy captured from the Sun. Humans and cows breathe out the carbon dioxide after the chemical energy is used.
Dissipates more quickly than what? Optimally, the cows would simply release carbon in the form of carbon dioxide rather than methane, since then you simply have a sustainable cycle:
Carbon dioxide is in the air. The carbon dioxide turns into grass. Some of the grass is used as an energy source by the cow, releasing the carbon dioxide back into the air. Some of the grass is used to make up the body mass of the cow, which is then used as an energy source by humans, releasing the carbon dioxide back into the air.
The point is that the carbon dioxide always ends up back where it started, so there's nothing inherently unsustainable. It's equivalent to growing a tree and then burning it (releasing carbon dioxide) to make use of the stored energy captured from the Sun. Humans and cows breathe out the carbon dioxide after the chemical energy is used.