"Death by natural causes" (i.e., death linked to old age, as opposed to premature death due to murder, warfare, traumatic accidents, etc) deserves to be approached and treated with grace.
To give you a specific sort of research that I feel is dangerous: preventing oxidative damage to telomeres (stopping one of the primary mechanisms of aging). Even though a breakthrough in that field will generate new therapies for schizophrenia and certain cancers, I believe that it will open a Pandora's box of externalities that, on balance, will outweigh the therapies.
I'm thinking about this more on principle: death is important for society in the same way that fire is important for a forest (imperfect analogy, but bear with me). The passing of older generations creates opportunities and mobility for younger generations, as well as room for cultural change that adapts with the rapid pace of technological change. I think in many ways the world would be a far worse place today were there large numbers of 120+ year-old people still around, voting however they would vote. Having a lot of 120-year-olds around would be ecologically untenable too.
In the original comment I refer to "grace", and by that I'm referring to the way that Randy Pausch or Morrie Schwartz describe their experiences with terminal disease. To them, death is an inevitability that highlights the value and sacredness of our short mortal lives. In the same way, I also really love the way how certain cultures treat funerals as celebrations of life rather than the somber sad traditions common in the West.
Put simply, death is what makes life valuable.
I personally subscribe in part to Professor Bruce Ames Triage Theory http://www.bruceames.org/Triage.pdf TLDR, is when a limited amount of nutrition in ingested, the body triages the allocation of nutrition. Now some of this will be caused simply by chemical chain reactions that have developed due to evolution but there is also some element of control by the body simply because the body can control things like blood flow, so when exercising, less blood goes to the gut and in extreme, you will see some athletes experience diarrhoea when exercising.
A cancer study I read by a Swiss Uni used radioactive B12 for thyroid cancer because the thyroid takes up B12. Its radioactive so it can show up on the scanners and they found the B12 was distributed throughout the body, it did not exclusively go to the thyroid. So yes Professor Ames is correct with his theory but it is not applied to every part of the body, otherwise how do you explain the Sodium Potassium pump in cells which dumps nutrition out of the cells with too much sodium? https://en.wikipedia.org/wiki/Na+/K+-ATPase
There is a saying, "you are what you eat" which is largely true, and whilst legislation in some countrys prevent some supplements from being sold due to the fact they have a pharmacological effect on the body, there are also external factors at play as well, like the domestication of our food, pollution and modern day living in general.
Anyway you could argue we already have that Elysium two tier society right now, but I think its possible for most westerners to afford what's necessary to increase their lifespan substantially. Developing countries are a different thing. However your point about death by natural causes being treated with grace is important. Its quite likely many old people will be dying with a lifespan in their 70-100yr range, but people in their 40's or less could well if the right interventions were made, live to be 150+. That's because of things like the internet improving communication, silicon chip, improved manufacturing processes and the ability to use search engines to read the latest studies from any part of the world that have been published just last month! It seems like something out of science fiction, but increasing lifespans is just one of those things that could be happening right now.
It also increases other problems though, namely if everyone were to live a US lifestyle we need 4 planet earths, 2.5 planets for a UK lifestyle and 2 for a European lifestyle, so people like Elon Musk, Jeff Bezos and others trying to get into space more efficiently and explore is like the olde worlde sailing ships setting off to explore the unknown.
Whats sad is knowing your parents wont enjoy the rude health the younger generations could be enjoying and many will have struggled to bring you up even though their conditions were even better than those before them, but that is probably best summed up as human progress.