Being human, we are always trying to find a way to improve our condition. We’re never satisfied with the status quo.
One very important metric for improvement is life span.

I found the above graph in a paper by Marvin Minsky. It shows that only about 20% of people lived to see age 45 in ancient Rome. By 1900, 20% of people lived to just above age 70. By 1960 20% made it to age 85.
Check out that last “all diseases cured” curve. If we cure all diseases (all diseases, that is, except aging itself) 20% will make it to 95. So if you’re part of that lucky 1 in 5, curing all disease would give you only 10 years more than you would have had in 1960. And the maximum life span hasn’t increased at all.