The part I highlighted isn't claimed by evolution. There is no sense of "best trait", just "best fit" (and even that's hyperbole, it's closer to "the best fit that needed to be found in order to survive and thrive"). Monkeys and non-human apes still exist because their adaptation was sufficient for them to survive in their particular little neighborhoods of whichever forests or savannas they live in. That is, they have a niche that they fill in some ecosystem. As long as that ecosystem continues to exist with only small changes, as long as the status quo is maintained, as long as the population isn't threatened, there's little adaptive pressure to drive big changes in the population.
Monkeys exist because there's still monkey-friendly forests in the world, with food monkeys like and with few enough deadly diseases and with predators monkeys can avoid often enough to keep their numbers stable. Human ancestors lived in different places or filled different roles in the ecosystem, were put under different adaptive pressures, found different tricks and adaptations to survive and- at some point before recorded history- found the combination of very large brains, long infancies, stable social structures, and trainable habits like speech and tool-building that let modern humans expand far, far beyond our original habitat and live almost anywhere on dry land on the globe. Our adaptations have now made virtually everyplace our habitat, and the pressures we're putting on other species- like some monkey species- are now driving them toward extinction. It's not the fact we live somewhere on the globe that's doing this, it's the fact that we're changing their habitats, and they aren't adapting vigorously enough.
Finally, you shouldn't think there was originally a colony of normal, modern apes (chimps or bonobos or something) and, gradually, some of those apes turned into humans. Evolution doesn't claim that. It claims modern apes and humans have a common ancestor- there was once a colony of creatures that were pre-chimp and pre-human (both, at the same time) and some of the descendants of these creatures are modern chimps and some of them are supermodels.
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