What would be the harm?

[Angrboda]

As has been said of Harris, you think that you've solved the perennial problem of objectively grounding morals when instead you've simply done philosophy badly

I haven't watched Harris in a while, but I don't think he's actually arguing that morality is intrinsically objective.  I think he's saying that we could choose, if we like, to base morality in an objective metric, like hedonic state, and that this would be much better than the false dilemma: believe that God dictates moral truths, or watch the entire world burn in anarchy while everyone just does whatever they want.

I could be wrong, though.  I haven't read his books or anything.

The Moral Landscape: How Science Can Determine Human Values is a book by Sam Harris published in 2010. In it, he promotes a science of morality and argues that many thinkers have long confused the relationship between morality, facts, and science. He aims to carve a third path between secularists who say morality is subjective (e.g. moral relativists), and religionists who say that morality is given by God and scripture. Harris contends that the only moral framework worth talking about is one where "morally good" things pertain to increases in the "well-being of conscious creatures". He then argues that, problems with philosophy of science and reason in general notwithstanding, 'moral questions' will have objectively right and wrong answers which are grounded in empirical facts about what causes people to flourish.

Wikipedia || The Moral Landscape