A common error about CH4 is misunderstanding half-life vs CO2e calculations. The half life is 10 years but that does not make it a non-problem; a commonly used number is that CH4 is 25 more potent that CO2 -- but that number 25x is OVER A 100 YEAR LIFESPAN that already INCLUDES the decay over those 100 years. So if you mention that half year is 10 years you also throw the number 25x out the window, then the multiplier is much much larger (forgot how much). Because of this scientists use different potebtial multiplier for CH4 for different time horizons. Anyway it IS a problem to have CH4 instead of CO2, how big a problem depends on your time horizon and over 100 years CH4 is 25x worse than CO2 INCLUDING decay.
You touch on the second point already. As long as lifestock is constant, CH4 is constant at a certain level. Still: Reducing lifestock will reduce CH4 to a lower constant level which will reduce greenhouse effects as CH4 decays to a lower stable level where emission and decay balance.
In a sense, reducing lifestock is the same as CO2 capture -- not the same as stopping to burn fossils.