Among the more obvious reasons I can think of:
* Pain makes it harder to think clearly. People who use their minds more vigorously tend to keep them in good shape. People who can't are more prone to losses, just as they lose muscle mass if it hurts too much to move.
* Pain is isolating. Other people often avoid those in pain, and someone who hurts all the time may not want company. Unfortunately isolation correlates with depression and other mental issues that undermine how well the brain works.
* Most, though not all, chronic pain comes from a systemic body problem, such as arthritis. Such problems tend to worsen health in general, not just the system where they manifest most visibly.
So that sucks, especially since pain and dementia are two things that modern medicine doesn't treat very effectively. What's worse is that current culture is drastically reducing access to painkillers, which hits people with chronic pain hardest of all.