Brain and body go together. Other animals have adaptations to their ecological niches. We have our adaptations to ours. Powerful brains are one of our adaptations to our niche, and an organism that has to live in our niche without our adaptations isn't going to do very well.

As soon as the cognitive capacity is sufficient for survival in some particular environment, there won't be any pressure for improvement of that, because it might in fact lead to maladaptive consequences, such as rise in depression and psychiatric disorders. Instead, there will be pressure for some physical fitness, improved immunity etc.

That's a misconception. The role of the brain our biology is not to direct somatomotor behavior, but visceromotor behavior. That is, the brain regulates the inside of the body. Increased cognitive capacity is largely directed to improving metabolic efficiency, immunity, and other basic bodily functions -- manipulating the external world is a bonus.

The higher levels of human intelligence are more useful for navigating the social than the physical environment, and obviously the social environment can vary drastically depending on where you live.