This is not why acetaminophen (aka paracetamol in UK & other places) is combined with opiates in compound preparations. Acetaminophen is an effective painkiller and it works in a different way to opiate drugs meaning that you take a smaller dose of opiates to get the same effect on your pain. Opiates have more side-effects (e.g. constipation, nausea) and also the problems of addiction and tolerance. NSAID drugs like ibuprofen can also be combined with acetaminophen meaning you take a smaller dose of them (they can cause damage to the stomach lining and kidney amongst other things). Paracetamol (sorry so much easier for me to type) is very well tolerated, side-effects are much rarer than other analgesics - its only major downside is that its so damned unpleasant in overdose.
Paracetamol is really commonly taken in attempted suicide and also overdose as a 'cry for help' in the UK. Its really heart-breaking how many patients i see who take an overdose, wake up and regret it only to have their liver slowly fail over the next few days and sometimes die a horrific death. Unintentional overdose with paracetamol is much, much rarer.
Despite this, i will always prescribe paracetamol to people who are in MASSIVE amounts of pain (cancer, post-op, palliative, trauma) as a first line in combination with other painkillers. Yes on its own it will only help with mild pain but thats not the point. Some people here seem to think that their doctor is precribing them something ineffective or trying to con them. That just isnt true.