It wouldn't be much more of a change than the impact of modern hygene. We already live many many times longer than during the dark ages, and even a fair bit longer than we did in the civilisations preceding the dark ages (Roman, Greek empires, where their knowledge of medicine and surgery was nothing to be scoffed at).
In every culture - with no exceptions - as the expected lifespan has increased, birthrates have decreased. That's why the nations with highest life expectancy have the lowest birth rates, and for the most part have shrinking populations. It stands to reason that the end of aging wouldn't lead to increased overpopulation, but rather a massive drop in reproduction, keeping population pretty much in check.
Look it up yourself - the nations with longest lifespans have shrinking populations. No, it would not be a problem at all for overpopulation.
As for the philosopical issues - surely that's something for the individual to contemplate in conjunction with his/her loved ones and advisers.
What it WOULD lead to is a new life stage, where you've raised your children and now have the financial means to pursue your life goals without the burden of familial responsibilities. Except people to have very few children, and then spend the rest of their lives aiming to become authors, artists, travellers and so on; living their dreams without the repercussions of responsibility.
Frankly (so long as our history-lond trend of increased lifespan leading to decreased reproduction keeps functioning), it seems like the recipe for a new human golden age - the means of actually ACHIEVING the enlightment project of the 1700-1800s, except now with our knowledge of cultural diversity and respect of indigenous cultures. We could actually take up the reigns of the old enlightment philosophers, this time untethered by greed and the insecurities of mortality (plus we'd have to take responsibility for the future effects of our choices upon the environment and the economy).
I have my doubts about whether that could ever be possible, but I sure hope that I live to see that day.