Allright... new statistics!
Health and Death
A total of 4002 characters were observed (from age 16 to death) regarding their life expectancy based on health as the variable. Other variables, such as epidemics, assassinations etc. were eliminated. There were two sets of samples, one with a health value of 6.00 which is pretty much the highest base health any character can achieve without trait/event modifiers. The other set had 5.00 health, which is the average base health of males. All characters were males, but sex here is irrelevant, the only advantage females have is their average 0.5 higher starting health. They live longer because their base health is higher on average. I should have done a 4.00 health set (which is pretty much the floor) but this experiment was pretty annoying to do (requires to actually process 90 years ingame)
Findings:
1) There seems to be a flat 4.5% chance that a character will have a mortal illness irrespective of health. Ironically this percentage was higher for the high health group, but that is just statistical randomness I think.
2) This one is a bit difficult to understand. The game distinguishes between 3 types of "natural" death. In case of "Natural" death, the character just dies apparently without any reason. The tooltip on the skull icon also says this. Someone here on the forums or reddit, can't remember pointed out that the game has a "culling" system: it does a health check every once in a while, and kills off characters who cannot make the check. The check is per individual, that is why you see people with cancer outliving healthy characters. It was also found that there are age brackets. Characters who are killed by this random check and are below age 45 automatically get the "Poor health" reason instead of the "natural death". It is possible (though very unlikely) that a Ruler Designer character with a health of 20.00 dies in a year in "poor health". The third type, "Trait" are deaths related to the character having a trait that is used as an explanation for death. The culling is the same, but if the character has a health condition, it is given in the tooltip instead of "natural".
So, without epidemics, characters on average have a 0.6% chance (for 6.00 health characters) or a 0.9% chance (for 5.00 health characters) to develop a health condition on their own, without any epidemic and die from that condition.
3) Approximately 4.5% are killed of before the age 45 by the culling.
4) The average age of characters with 5.00 health is 63.8 years, 68% falling into the 62.1-65.5 year range. Median is 65 years.
5) The average age of characters with 6.00 health is 64.8 years, 68% falling into the 63.0-66.6 year range. Median is 66 years.
6) It appears, that 1.00 health translates to one additional year lived on average, BUT most likely this is NOT linear. I expect that characters with 4.00 health would live MUCH shorter on average than those of 5.00 or 6.00, not just 1 year shorter on average. This is because they are more susceptible to developing conditions on their own, not to mention they are very unlikely to survive epidemics.
NOTES
The experiment did not include child survivability. Much like in real life, taking child mortality into account, that 1.00 health would have made a much greater difference as low health characters are very likely to die before age 6 (this is hardcoded in the game, the culling system is harsher for infants and people over 70). My suspicion that a character with 4.00 health is quite unlikely to survive childhood.
The experiment also excluded epidemics. They cannot be really tested because epidemics are extremely random (when, where and which sickness occurs). My guess is that epidemics on average lower the life expectancy by around 10 years.
CONCLUSION
My unsubstantiated estimation is that life expectancy with Reaper's Due epidemics and child mortality should be around the age of 50. War and assassinations also need to be included, but again, they are very arbitrary. The conclusion is, that expecting your ruler to reach age 60 is not a good strategy. Make sure you have a competent heir ready to take over when your ruler hits age 45.
So, the value of the health attribute largely depends on where you rule. Rulers of coastal regions are much more susceptible to epidemics than those deep inland making the health attribute very valuable to them. If you are in the very middle of the HRE you can focus more on other attributes.