It's more efficient, but the end result is basically the same, especially considering that even if there's no noise in the optimization algorithm, there is stil

It's more efficient, but the end result is basically the same, especially considering that even if there's no noise in the optimization algorithm, there is still noise in the gradient information (consider some magical mechanism for adjusting behaviour of an animal after it's died before reproducing. There's going to be a lot of nudges one way or another for things like 'take a step to the right to dodge that boulder that fell on you').