Aging is probably an important factor in some games, but I'd probably lump it in with eating/drinking, sleeping, and torches. They may make a game more realistic, but not in a fun or interesting way. That doesn't have to be the case, though. I can imagine scenarios where timing is important, so that you need to plan your campaigns around seasons. That has definitely been a factor in real-life military history, where the seasons played a pivotal role (thinking of the two major invasions of Russia in particular). I could see a type of "campaign planner" in an RPG where players had to think rationally about when they wanted to embark on certain quests, perhaps choosing them based on their location and time of year.

It's also arguable that people aren't affected by aging as much as some might think. In my martial arts course, for instance, we find plenty of examples of older men who seem just as able as younger ones. I guess eventually sheer muscle atrophy and the like will degrade their performance, though it may turn out their incredible muscle memory and experience will trump a younger man's extra speed or strength. In any case, a 70-year old black belt who has been actively training since his teenage years would be a formidable foe regardless.