The logical implication being that wizards are not overly concerned about old age, because very few of them ever die from it. Something else - A dark lord, screwing up a spell, the magical wildlife, a succession dispute.. will get you first... This logic could well deter a lot of people from attempting alchemy ; Succeeding in making a stone without being as good a survivor as Flamel carries a significant risk of dying now to violence instead of in 90 years to natural causes.

For that matter, screwing up an attempt to make the Philosopher's Stone might very well be one way to invite a premature death. Alchemy isn't necessarily safe.