I think it's a little weird to assume that's how everything is "supposed" to be just because that's how it's been. There's really no "supposed to"; there's what there is, and what we can do and change and build.
I do agree that some people take this to far: worrying so much about death that they forget to enjoy life, pouring their lives into life-extension measures and leaving precious little time to live. (Then again, the people who pour their lives into life-extension could end up benefiting countless others; how's that for big-picture thinking?) But I'd hardly call it a "tragedy" that humans want to live longer (or even forever).
I don't particularly fear death, I don't think (at least not any more than your average human), but I am supremely bummed out that (assuming humanity doesn't destroy itself first) I'm going to miss out on things like advanced spaceflight, viable long-term colonization of other planets and moons in our solar system, and -- if we can figure out that pesky speed of light issue -- travel to and colonization of other solar systems. And that's without getting into more "out there" stuff like mind uploading and catoms and whatnot. Humanity has so much potential, and we're still a childishly young species that has so much room to grow. To me, the tragedy is that I won't get to see what happens with all that.
I think the bottom line is that we should stop judging people for how they use their time. I'm sure there are some people who would scoff at some of the things you or I do with our time; who are we to criticize someone for working to lengthen the human lifespan?