I believe it depends on the circumstances involved and the length of time apart between the couple as well as their mindset today.
It's unrealistic to expect "instant friendship" after a breakup. Odds are if this is attempted the hurt person secretly hopes to win back their ex unless the breakup is the result of them having been cheated on or mistreated.
The best friendships between exes usually occur after there has been a large gap of time and both parties have moved on and found love with others. If it still hurts you every time you see them it means you have not gotten over them. True forgiveness means letting go.