So tell me, is there any contraindication to treating pain? No! There may be contraindications to specific medicines, but not to pain in general.
Have you ever tried to examine somebody who is in writhing agony? I have, and it's pretty bloody hard let me tell you. That's just examining them, let alone getting them onto the bed and down to the ambulance and drive them to hospital.
When I first started it was entonox and morphine, and ketamine had just come out; so pretty limited. I can remember morphine plus midazolam because not everybody had ketamine. I don't even think there was paracetamol. Now there's almost no reason pain can't be treated between entonox, methoxyflurane, paracetamol, ibuprofen, tramadol, morphine, fentanyl, ketamine, and lignocaine blocks.
"Don't treat abdominal pain" is a relic from the decades before high-tech imaging such as CT scanning when surgeons had to rely more upon physical examination. As an aside, my ability to examine abdomens is absolutely terrible. I can inspect, auscultate and have a push in the 9 quadrants and have a general idea of what is in each but I'm really not very good. Most patients with abdominal pain "bad" enough to ring ambo gets taken to ED where they'll probably get thrown through the CT scanner (maybe) so nothing I really do is going to be clinically significant in terms of a diagnosis.