@gizzy oral pain relief is quite necessary in many cases, and for various reasons.
Firstly yes, they DO hide their pain. Of cause if you cut a pig's nails to the quick the guinea pig will flinch/squeal as is reacting to a sudden shock and pain that the pig was completely unprepared for. In the wild a prey animal in pain would be one more likely to be picked out as being easier to catch by a predator, so many animals will hide their pain. Their instincts are still strong to this day in this regard, but it doesn't mean the pain is not there.
As for receptors in the brain - I assume you have scientific evidence to back this up? Of course every single species is different, but actually so are human individuals. If you wish to quote one example of a human taking a long time to do the 'necessary deed' then bear in mind there are other examples of humans who have done so much quicker. For an animal the instinct to survive a harsh situation will call for a harsh and painful decision, and may do so quicker as they are not thinking the process through as much as a human will. An animal will not ponder the possibilities of a fatal bleed from their amputated foot, nor the hardship it will face from losing it. The animal will totally believe that if he doesn't amputate his own foot then he will die. Fear of death is strong enough for animals to get through the necessary task, humans have other fears added to this and will weigh up the pros and cons before taking such drastic action. Animals will be seen gasping in dreadful pain and yet carrying on with trying to escape as their fear of death is a stronger motivation than their pain. You will find many such cases with humans too, in such great pain but their motivation to try to survive is greater than their pain.
To claim that an animal doesn't feel pain enough to warrant pain relief is very misguided to be honest.
Now pain relief itself. Guinea pigs have been known to lose their appetites due to pain. Many of us have witnessed this, many vets know this. To let a pet continue through their pain also causes a greater amount of stress hormones to be released into the body, and these can also harm their health. This is known. Stress hormones increase inflammation, just one example. Continued inflammation can cause damage to surrounding tissue and will hinder the healing process, sometimes permanent damage can occur. A continued raise in heart rate and blood pressure is another result of being in a prolonged state of stress. None of these things are useful when trying to recover from damage or illness.
Then there's sleep. Sleep is a great healer, it's not just a saying, it is true. A lot of healing is done whilst sleeping, and pain of course has a lot of potential to keep one awake, whether that be an animal or a human. Lack of sleep causes added health issues and added physical stress, as well as mental stress.
Some pain killers actually do a secondary task - Metacam for example helps to relieve inflammation. I see what you say about opioids, but in cases of severe pain sometimes nothing else will touch it.
In the case of Metacam though, this is not an opioid, it is an NSAID (Non-steroidal anti-inflammatory drug). Other NSAIDS used in humans include aspirin, ibuprofen and naproxen. Whilst we all must weigh up the pros and cons of taking meds and must make that decision for those who cannot make it themselves, Metacam is generally very well tolerated in Guinea Pigs and the benefits of the pain relief and anti-inflammatory aspects, and the reductions of stress etc, are well known. Going further when weighing up the pros of cons for those who cannot decide, it's important to remember that vets have studied the mechanisms of how medications work. They will understand the benefits when prescribing these meds and will know more than the average pet owner. By all means question, and they will explain, but to go against the advice can be detrimental to your pet.
Sorry
@gizzy but whilst it is an undisputed fact that many medications have either definite side effects or potential ones depending on dosage and the way each individual body reacts and the type of medication, the benefits are well and truly known, as are the detrimental health affects of leaving an animal, or a person, in a state of continued pain and distress. Some of what you have stated is incorrect, I'm sorry to say, and some seem to be assumptions based on a few documented experiences instead of the big picture overall. Going against providing pain relief based on not knowing the big picture and the full facts is quite frankly potentially damaging for pets. Anyone knowing the full facts will see that there's unlikely to be many, if any, situations where it's best not to provide pain relief, and assumptions that they do not feel enough pain to warrant relief is simply not true.