This doesn't prove that our morality is objectively better - it's impossible to prove this, by definition - but it does dismiss the implication of the argument that "you like today's morality because you live today". Only the people who live today are likely to like their time's morality.

Thanks, this is a good point - and of course there's plenty to dislike about lots of morality to be found today, there's reason to hope the people of tomorrow will overall like tomorrow's morality even better. As you say, this doesn't lead to objective morality, but it's a happy thought.