I suspect high intelligence might be a short-term species-level adaptation to existential threats that would otherwise not be expressed nearly as often in healthy populations. There are smart people, and then there are people who can’t help but be neurotically fixated on problem-solving - and this latter group often suffers through their lives due to how different their experiences are from the norm. If some variation of this describes reality, then intelligence and mental health issues (or at least the burden of neurodivergency) may be fundamentally inseparable.

Ninja edit: But the reverse doesn’t seem to be true - one can suffer from mental illness due a variety of factors, including ones that we can (theoretically) actively and competently manage, like oppression and inequality.