Notably, a lot of the people I know who report depression-inducing pain have distracting, breakthrough pain.
Even with chronic pain, it's probably not the end of the world when it's "an ache in my knee when I move in this direction" or even "a mild ache in my knee always". But if it's "at random, frequent times, my back hurts too badly to stand or function", that's super hard to ignore or get used to, and I can see being incredibly upset by it. Cluster headaches come to mind as following this sporadic + devastating pattern, and indeed they do cause a fair bit of suicide.
"Can't escape it" and "can't get used to it" are an ugly combination.
Kind of like being short, or not as smart as the next guy. It's just the way it is. No point worrying about it.
However, if you viewed it as a serious problem and when is it going to be fixed and then... never... yeah, that would be very different.