Accepting mortality is important for a lot of reasons I find difficult to explain properly. It's a matter of shared context being the basis for communication and the requirement for a whole lot of concepts to have to be understood by both of us, and referenced by the same words, to convey actual understanding. It is difficult, for instance, to separate the topic of mortality from the discussion of the conception of self. I will attempt an explaination regardless.
Knowing, and accepting that your end is inevitable is important context for how you choose to interact with the world. Let's try a thought experiment: There's a version of the world you want to live in, and there's alternatively a version in which you don't, right? Since you will someday die anyway, it makes no sense to survive at the cost of moving the world towards the version that you don't want to live in. If you don't accept that the end is inevitable, you can justify such acts anyway because you'll always be able to move the world the other direction later, just as soon as the current existential threat is dealt with. Only, of course, there are always more existential threats, whether real or imagined.
Many atrocities were and are committed in the name of survival, whether of an individual's physical self, or one of their shared memetic selves like culture or society, their genetic self embodied in their children, or sometimes even more raw memetic concepts. That's the "rational" way of interacting with the world. You have a goal (survival of some conception of self), and you do anything to achieve that goal, because rational approaches do not accept failure as an outcome. Accepting mortality is recognizing that the goal is ultimately unachievable, and because of that, there are potentially things of greater value than survival. You don't have to survive, failure to achieve that goal is an acceptable outcome, and you can choose to interact with the world differently.