The human brain isn’t “more” evolved. It’s just differently evolved. Our intelligence has its obvious advantages, but it carries some significant costs. Like Joshua Engel says, the big brain is metabolically expensive. It makes childbirth much harder for humans than for other mammals, too. Human babies have to be effectively born prematurely in order to fit the big head through the birth canal, and even so, it takes years for the brain to develop to the point where a person can function on the most basic level. Other mammals are up and walking in a matter of hours, and are ready to fend for themselves after a few weeks.
Our smaller-brained ancestors survived fine on the African savannah for millions of years. The growth in our cranial size has been explosively sudden in evolutionary terms. Susan Blackmore has a theory that the bigger brains aren’t necessarily for our sole benefit. She thinks we’re co-evolving with memes, information viruses that are symbiotic and/or parasitic with our brains the way our gut flora and fauna are symbiotic and/or parasitic with our digestive tracts. She posts a sexual selection theory: having more memes in your head signals greater reproductive fitness, and bigger brains can hold more memes, setting off the same kind of self-perpetuating cycle that resulted in birds of paradise having absurdly long tails.
The big brain has been an advantage against other megafauna during very recent evolutionary history, but it might not be that big an advantage in the long term. Consider this: brainless microbes have been around for four billion years, surviving asteroid impacts so big that the oceans boiled away. There have been jellyfish with simple neural nets for six hundred million years, and cockroaches with tiny brains incapable of learning for four hundred million years. There have been humans for only two hundred thousand years, and we’ve shown evidence of abstract thought for only the past forty thousand. In this geological eyeblink, we’ve exploded our population and our global range, so good for us, but we’ve also caused a global extinction event that might eventually wipe ourselves out too. If we do, the microbes and cockroaches will barely even notice that we were here.