The reward for big brains may not be art, culture, comfort, or even basic survival. Instead, it may just be the development of larger penises.
The great apes are bigger than humans in a lot of ways. A lot of them have overall size on us. Because they're not sitting around in swivel chairs all day they generally have bigger muscles. But there are at least two parts of the human body that surpass our ape cousins' in size: heads and penises. It turns out that these two things are not unrelated.
Tiny little chimp brains can be contained in tiny little chimp heads. And tiny little chimp heads can be easily birthed. As humans needed larger brains in order to acquire language, imagination, and the ability to learn, their heads needed to expand along with everything else. In order for large-headed human infants to come out of human females, the birth canals of human females needed to expand.
These expanded birth canals meant competition was on as to whose sperm could get to the end of it in order to do some impregnating. There are only a few ways to do this. Either super-charged sperm can race down the birth canal or regular sperm can be given a 'head start'. The larger heads of infants lead to larger birth canals, which in turn lead human males to have much larger penises than the great apes.
Just don't tell that to a silverback gorilla.