Ideally I'd avoid the pain altogether to begin with if I could, but I reckon its essential that we're able to still detect/feel the pain if it isn't something that's not a relentless constant in which case it would be more appropriate to take pain killers as it could have an inverse impact on health much in the way that depression can. The idea that someone could die of a broken heart in combination with ill health isn't all that far fetched but that's a whole other can of worms that's labeled psychology.

For example,  I recently suffered from severe lower back pains, my initial guess is that it would most likely have been caused by a slipped disk but there were a fair number of things that led me away from that conclusion but that’s another story. Whatever the case it wasn't a constant pain that was present regardless of what I did although the pain was actually initially present for a lot of the time. Eventually it began subside whilst generally trying to do as little physical activity as possible. The only time it stopped hurting was when I was stood with the correct posture or lay on my back with the plates of my shoulder blades flat to the solid ground and not on a soft bed whilst trying to catch some z's. It basically meant my spine was arched in its correct position reducing the pressure to my lower back if I laid still. (This is not the same as enduring actual constant physical pain, in which case there definitely is something wrong) Of course it also meant that I couldn't really deviate to much from that position either whilst lying down. Initially trying to get some sleep on a soft bed would have been much uncomfortable then laying on the flat solid ground.

As I said before it was still possible to walk around without any pain provided I used the correct posture. I just couldn't bend down at all or sit for too long in the initial stages.

If I had in fact taken pain killers to mask the pain I would probably have ended up trapping the inflamed nerve whilst going about my day without knowing it to have then caused it to become even more swollen which in turn would have then made it even more painful once the pain killers had worn off. In this instance the pain acted as a guide as to what I should avoid doing whilst waiting for the swelling to go down and my body to clear out what ever it was that was causing the the pain in my lower back. As the pain wasn't an unavoidable constant relentless pain that was present regardless of what I did I didn't feel it was necessary to take pain killers.

A much simpler analogy would be if you were to put your hand in a fire and you were completely impervious to pain, you would have no hand left if it was in fact dipped in a blaze without you realising it for whatever reason.