You say that, but it's not really just about grass-feeding. Cows are already fed almost 90% inedible crop materials that would be getting disposed of anyway. We could be doing better, but cattle's food source is sorta the wrong focus.
And as much methane is in manure, it's better for the environment (including GHG) than synthetic fertilizers.
The real answer is changing our meat/vegetable balance AND improve the process AND continue to improve humane regulations (and those 3 goals often synergize with each other).