Most Helpful Guy
Unless the breakup is entirely mutual because both parties have just been going through the motions then no. If it's two people who can literally say look, we're not really feeling it anymore so let's go our separate ways, and nobody is feeling angry or hurt or regretful, then it can work. In the vast majority of breakups that's not the case.
The impulse to suggest being friends is generally said out of guilt on the part of one and out of hope on the part of the other. It's not realistic in most cases. You can't get over your pain if the thorn is still in your side. You have to extract it in order to heal. Maybe then in the future you can look back and laugh together.