Consider that it might be to the benefit of the reader to hear all the different possible ways of expressing the different arguments and counter-arguments, even when the participants themselves don't budge.
Also, I often find that while I don't usually change my opinion in the middle of an argument, it still helps me to have the weakest areas of my opinions highlighted so that I know not to invest too strongly in those aspects as time goes on. After reading a compelling counter-argument online and then seeing first-hand evidence of the strength of that counter-argument later on, I think I'm much more likely to change my opinion.
During an argument I think it actually benefits all participants to stick to a consistent viewpoint and defend it as strongly as possible to make sure that its strengths and weaknesses are fairly represented.