But that's not what OP is about, and it suggests that's not really what the research says either, there's maybe a bit of hint of a small negative correlation like that, but mostly it says: no correlation.
Rather than making the argument you are making, which I have heard before, I found the OP argument to be novel to me, and find really thought-provoking:
The model of "well-defined" vs "poorly-defined" problems, and that what we call "smart" is skill at solving "well-defined" problems, but that happiness actually depends on skill at solving "poorly-defined" problems. Which is probably not correlated to skill at solving well-defined problems at all, that being "smart" at solving well-defined problems doesn't help or hurt happiness, it just doesn't matter.
This rings really true to me, and isn't quite as depressing as the oft-heard theory that you're saying here, that smart people are more likely to be miserable because they see the awful. Not what OP is saying, OP is even disagreeing, really.