I think leading with either foot is essential. Particularly, it’s important for beginning a climb or hopping up something where you will have to change your rhythm if you need to switch to lead with a particular foot.
That said, I can’t always make it work in practice.
It’s perfectly natural to have a dominant foot, just as we have a dominant hand, ear, eye etc. the human body, including the brain, is asymmetrical. Otherwise we would all be completely ambidextrous.