There are real drawbacks to living in an oxidizing atmosphere. You rust. That's aging in a nutshell - the stuff that makes you work bleaches in the sun. As soon as we committed to hemoglobin we committed to an expiration date and I'm unaware of any critter that's gotten around that.

Maybe. But there's a lot of evidence that oxidation is not really the primary cause of aging, and that it's easily gotten around. No, the 'real' reason we age is because we've evolved to age. Take mice and humans, for example. Our basic biology is essentially identical, yet mice live 2 years if allowed to complete a full life cycles, while humans can live 40 or 50 times that. Energetically speaking (I know you're a thermo guy), it's actually much less costly for an organism to repair oxidative damage than it is to reproduce, which entails growing a whole new being, a being that is now also going to compete with you for resources. So, then why go to all the trouble of growing old and dying when there's no real biological reason it has to be that way? Because the very nature of biological evolution (descent with modification, in Darwin's very much more apt parlance) requires replacement. If we were perfectly suited to an environment, we could live forever. But even in that case, the environment will change eventually (or a new disease will crop up, or whatever other catastrophe), and the species will be wiped out in one generation. The species that have survived through the eons are the ones that have found ways to deal with small and even large changes in their niche. Therefore, the reason a mouse matures in 2 months and dies in two years, while a human or an elephant does not, is because that is the most stable state in which they can exist. It's an evolutionary strategy, so to speak (even though I hate to use terms that imply design; it's use is metaphorical).

Whether it's oxidative stress, telomere shortening, or the several other specific mechanisms that contribute to decline, they don't answer the question of why we age, which is a way more interesting question. We age because it makes sense. In the end, the idea of living forever is not only stupid and pointless, it's downright harmful.