Its not crazy to think that, if we live that long, we will figure out a way to escape even the end of the universe (I'm reminded of Asimov's The Last Question). But that progress definitely won't happen if future generations can't build on what we've learned.
I actually think living with the idea that everything is temporary is very very dangerous. Nothing is temporary, except you. We need to live with the humility to recognize that our life on this planet is incomprehensibly short, and we need to spend it doing everything we can to give our children the headstart they need to do everything they can to give their children a headstart... into infinity. That's the only way we improve as a species. That's why there is no greater sin than destroying or limiting access to information, and conversely why the internet is literally the most substantial development in the history of mankind.
The Last Question is a work of fiction. All works of fact seem to support the concept that it is not possible. That isn't to say that we will never discover properties of the universe that open new possibilities, but A) I think eternity is just a different kind of ending anyway, and B) stubbornly grasping to such a concept seems a desperate attempt to deny one's own mortality.
I'm not advocating for forgetting things for the sake of it, I'm advocating against the idea that everything must be preserved. Certainly we should try to keep in mind the lessons of our past, but we should also be willing to let go of things that haven't given us good reason to keep them around.
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.
That said on the topic of conservation, or more accurately History, I don't think you can convincingly argue for forgetting things as a society. The cost of repeating errors are as great as the benefits of safekeeping knowledge.
You mention physics. A constant in our universe is that things decay unless actively maintained. All life is fight against entropy. Trying to preserve things is only natural.
We put priority on benefits we can realize. Short term benefits are easier to realize, and decisions made in the moment, absent malicious intent, make sense in the moment. Hindsight, as they say, is 20/20. We make a prediction now what will be important later, sometimes we are right, sometimes we are wrong. Perfection is impossible, and even if it weren't, it would not be worth the cost of trying to attain it.