It is perhaps easy to overlook the fact that the modern standard of "fair" is far subtler than the ancient standard of "fair". Social mobility, human rights, effective medicine, myriad technological comforts all make our lives unbelievably more "fair" than contemporaries of Seneca would have ever likely imagined.
And yet you suppose that Seneca was unaware about the "unfairness" of the universe. Ah, but you misinterpret the essay. The point is not to convince you that your life, or all human life, is unequivocally "fair" - as certified by some mystical fairy God dancing in the Cosmos - but to convince you that the only way to maximize the "fairness" of your own life is by the action of the individual, by the application of correct concepts of human morality: by proper ethics.
As pertains to the subject of this essay, this means to act as if your life is of sufficient measure for you to fulfill yourself only if you do not waste it.
Moreover, to respond to your general dismissal of the essay, Seneca is writing on a particular instance of "unfairness" - the shortness of life, not all "unfairness" (e.g. being born with a genetic disorder). Of course, the Stoics were keenly aware of this type of "unfairness" as a defining characteristic of the human condition. Indeed, much of their philosophy is devoted to it. But a discussion of this would take us much too far afield and I'm afraid you would not be interested ...