(if we can objectively characterize human well-being, it absolutely is in the domain of science)
What does it mean to "objectively characterize human well-being?" Human well-being seems to be an incredibly value-laden concept, in fact, I can't imagine how it could not be.
Religion has been rolled back on all its truth claims regarding issues belonging to science, and is making its last stand of validity on claiming to be the only source of morality. Knock that pillar out from under it and the whole stinking artifice comes crashing down, the sooner the better. So now, if someone raises the "But where else can we get our morals except religion?" question, there's a valid place to point. That alone makes Harris' work extremely valuable because he is bringing the proposition into popular consciousness.
I think Religion's "last stand" is that it meets a sort of basic human need, and this need is much closer to a sense of purpose, order, value, and meaning than simply of morality. I don't think most religious people would assert that religion is necessary for many kinds of moral behavior, if asked "If you were to discover that there were no God, would you start raping and pillaging?" I think most would answer "no." There's abundant evidence that atheists don't commit more crimes than theists, and I don't think the general populace of America would be surprised at these findings. Morals need not have a source of authority, we might just "get our morals" from society itself. Supposing, as I do, that some sort of system of justification is desirable, we can evaluate two such types of systems.
The first is the sort which justifies itself on observation and argument, attempting to provide good reasons for everything they say and resting their claims on the merits of the case they are putting forth; and the second is those which appeal to some authority, those who demand credence on something other than rational grounds. The former seeks its validation from within and includes philosophy and science, the second from without, and obviously includes religion. The problem with Harris is that at times he seems to implicitly place philosophy in the latter category, and even at times when he does not, he fails to recognize the unique domains of philosophy and science. To attempt to use philosophical inquiry to answer scientific questions is as fruitless and misguided as using scientific inquiry to answer philosophical questions.
However, this clearly can and is done (prior to "science" existing as we know it today, things like astronomy were handled philosophically, with unsurprisingly poor results), but to do so necessitates a degradation in the quality of the arguments and a softening in commitment to rational explanations, often requiring one to take things on faith, since when using the wrong tools one can't build proper grounding. Thus, the very virtues of the system which seeks validation from within melt away when one conflates philosophical and scientific inquiry. By doing doing this, while enjoying the popularity and influence of riding the popular wave of intellectual-anti-religious-manifestos, Harris work is not only of little value, but is intellectually backwards and dishonest. The grounding for morality in a post-religious world is both important and extremely complex, but Harris's charlatanic views are intellectually holding back rather than pushing forward that inquiry.