Water 'purification' in most cases (on occasion it was boiled) did nothing to remove the tasteless toxins that can cause illness and water was mostly just judged by how clear it looked and how it tasted/smelled. Food safety again being something of a sniff/taste test. Vaccines of course would not be invented for thousands of years. Some of the quirks of their civilization included shared butt wiping sponges at public toilets - you'd clean off the sponge using either running water, or on occasion a bucket of vinegar. And so on.
The point of this is that if we provided these Ancient Greeks with nothing but urgent life-saving emergency care from modern technology, it's highly likely that their life expectancy would dwarf ours of today. So what exactly was it in their culture that we've lost? They did so many things so differently that we can probably all kick in some confirmation bias to support our own personal hypotheses for some particular subset. But I prefer to just look at things holistically and consider that aiming to emulate their lifestyles is probably a better overall way to aim for a long and healthy life than is relying so heavily on medicine and technology.
[1] - https://en.wikipedia.org/wiki/List_of_ancient_Greeks
[2] - https://en.wikipedia.org/wiki/Miasma_theory
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EDIT: Just, completely coincidentally, saw another related article here [3]. Anyhow, it provides an important datum: "More than 23 percent of Americans took three or more prescription drugs in the past 30 days, according to a 2017 CDC estimate. Furthermore, 39 percent over age 65 take five or more, a number that’s increased three-fold in the last several decades. There are about 1,000 known side effects and 5,000 drugs on the market, making for nearly 125 billion possible side effects between all possible pairs of drugs. Most of these have never been prescribed together, let alone systematically studied, according to the Stanford researchers."
[3] - http://www.kurzweilai.net/how-to-predict-the-side-effects-of...