My question from the outset was "what's the use of happiness?" Responding to that with "its own sake" doesn't answer my question. To say that 'being useful is useful for its own sake' is to make an intrinsic utilitity statement of utility.

My answer to this would be that happiness doesn't necessarily have any value outside of human brains. But that doesn't matter. For most people, it's one of those facets of life that is so basic, so integrated into everything, that it's impossible not to base a lot of decisions on "what makes me happy." (And variants: what makes me satisfied with myself, what makes me able to be proud of myself...I would consider these metrics to be happiness-based even if they don't measure just pleasure in the moment.)

You can try to make general unified theories about what should be true, but in the end, what is true is that human brains experience a state called happiness, and it's a state most people like and want, and that doesn't change no matter what your theory is.