So why didn't chimps get some of them?
For example, chimps have hands, but do not exhibit anywhere near the dexterity and agility of human hands.
Now if these costs are indeed less than the fitness advantage of a chimp having more dexterous hands, and that is in biological fitness as in reproductive success not the colloquial 'fitness' as in going to the gym, and that mutation for dexterous hands is present among the breeding population, you will expect to see offspring with that mutation, having higher fitness, to increase in frequency in the population.
There are a lot of potential edge cases to consider as well. Maybe the dexterous hands allele is very close to a very bad allele in chimps, such that through recombination it is likely that these two alleles are inherited together (called linkage). You'd see both these alleles purged from the population over time through purifying selection.
There is the population history aspect to consider. Maybe you don't need dexterous hands if your population is still living in the jungle among plentiful calories like the chimpanzee. Maybe it is more relevant to comparatively more feeble humans that were pushed out of that jungle by physically stronger ape populations into more nutrient poor environments, where suddenly the increased fitness from the advantages dexterous hands might bring now pay for their energy costs.
So it's not just brainpower, it's likely a combination of potential brainpower - which many species have/had - and fine motor control, which set up feedback loop that translated a mind/body synergy into practical evolutionary benefits.
The chimps that did get them we now call humans.
There were no chimps back then. We had a shared common ancestor, and subgroups gradually emerged and gradually became different enough that they stopped interbreeding (or were physically separated).