People will not do tasks merely because it's "fair". Otherwise crime would have evaporated, life would be harmonious, and judges would be bored.
I think that what would end up happening is that in even in a small group of people, it would naturally emerge that there are variations in quality, efficient, economies of scale, etc. Even in my immediate family, there are some menial jobs that my wife does 90-100% of and some menial jobs that I do 90-100% of. If we tried to make if 50-50 or have some type of rotation, we would both lose.
Because you recognize this and aren't completely inflexible, you don't. Some degree of self-organization for mutual convenience can be relied on in much larger groups of people than two. For example, I often hear of shift workers trading shifts.