Immunity is highly specific. This is why the flu is a chronic problem, it mutates rapidly enough that exposure to previous generations of the virus does not confer immunity to current generations. Immunity is more like a collection of solutions to puzzles than it is a muscle.

Being infected while in a healthier state and thus gaining immunity with less risk might be beneficial later, but you can look at mortality statistics and see that while infections are a major cause of death, they aren't responsible for a large portion of deaths:

http://www.cdc.gov/nchs/fastats/deaths.htm

(Chronic lower respiratory disease there is stuff like COPD, not particularly infection related)