It isn't just about depth perception. You lose peripheral vision on one entire side of your body and it upsets your balance.
And yet, even with that, the physical is still less important that the psychological aspect of fighting, which is where the good and bad are judged. Having fought a bunch growing up and as an adult, including actual combat with armed enemy, and from the knowledge I've accrued from reading about famous warriors of the past, and current ones (like SOF veterans), all who talk about the importance of it, I wholeheartedly believe in the absolutely necessity to have proper combat mindset, it is without a doubt what truly separates the best from everyone else. One can have a superior warrior mindset while missing an eye and still be a great warrior, whereas someone physically perfect, not just two working eyes, but incredibly athletic, in perfect health, tough and brave in many regards, can suck as a warrior simply for not possessing the right combat mindset.