Most Helpful Guy
Almost never works. First if all, any attempt at being friends has to wait until both parties are fully done mourning the loss of the relationship. That only happens quickly when it is less of a break up, and more just both acknowledging that the relationship died a while back and you are actually both already over one another before the breakup. It is very uncommon for that to happen.
Second, you both really have to honestly want to be just friends. Almost always when a couple tries to be friends after a breakup, one of them is lying about only wanting to be friends. One or another almost always is just pretending to be okay with being friends in order to win the other back, or constantly trying to make it friends-with-benifits. Now, if you both agree that you make an awful couple, but the sex is great, there is nothing wrong with keeping one another as a booty call as long as you both really are okay with that and acknowledge that sooner or later one or both of you will eventually see someone else.
The other case this can work is if you were already friends before you became a couple, and both realise that you make a bad couple. Then transitioning back to friends can be a natural thing as long as it's mutual.