Yes, the phrase is now a cliche and hence ubiquitous. You will hear that Darwin did not invent it but rather that Herbert Spencer, an English philosopher of the 19th century, coined it (see this link to learn more than you likely ever wanted to know about this phrase).
Yet, the idea behind the cliche is part of the mental furniture of many. But I have a few (really two) questions:
1. Question the very notion of "survival." Is that all that you are seeking?
2. Question the notion of the "fittest." Is it really the one with the most toys or the most power or the most sexual partners?
My counterproposal is this: the "flourishing of the humblest," in the sense that mere survival is too meager a goal for human beings who are endowed with so many wonderful gifts and that the key to such flourishing is exactly the very opposite of what we assume from our social, and even family, conditioning. We assume that the grasping individual who leaves no stone unturned in maximizing his or her possessions and pleasure is the model for our success, the model we must live up to in our lives. Many follow this model and pay secret allegiance to it, even though they would not want to admit to this deep allegiance in public. For one thing, admitting it in public may create difficulties for many individuals who pretend to be quite pious and religious or who pose as upright in secular settings.
The more I reflect on what I see and what I experience the more I conclude that the key to human flourishing is, ironically, humility. Pride is a prison. Humility is the freedom of the open air. Nothing fazes the truly humble. Many of you reading this post know that already and can confirm it. Spread the word. It makes for a better world.