The best friendships between exes usually occurs after a large gap in time. Essentially both people have moved on and found true love or real happiness with other people.
They're no longer "emotionally invested" in their past. It's almost as if they're grateful they broke up because it allowed them to find that special someone or even find happiness within themselves.
Having said that it's unrealistic to expect to go from being "red hot lovers" to "instant platonic friends" rivaling something along the lines of being brother and sister. Rarely is it a situation where both people wanted to breakup. Generally speaking the person ending the relationship is only offering "friendship" as a "consolation prize" in order to avoid feeling like the "bad guy".
However their ex sees friendship as a ray of hope that may lead to a reconciliation.
Hollywood movies and romance novels has planted the seed that loving/passionate relationships are filled with "drama" including breakups and makeups before there can be a "happily ever after".
In fact society tells us: "Relationships are (hard work".
The reality is if it's that "hard" you're probably with the (wrong) one!
Compatibility trumps compromise!
If either of you has to "change" to make a relationship "work" it means you're with the wrong person. People don't change unless (they're) unhappy.
The goal is to find someone who (already is) what you want.
Another reason is sometimes exes end up having sex. This sets up things for the dumped person to be hurt even more once they realize they have become a "booty call" or "friends with benefits" until their ex finds love with another. They truly believed the sex was leading to getting back together.
Lastly even if exes manage to become best friends eventually one or both of them will find new love with someone who doesn't want their man/woman spending time with their ex unless they have children.
It may be possible to become (good acquaintances) but don't expect to be "best friends forever".
Very few women I know of would be okay with their man going to lunch, to happy hours, or checking out an entertainment or sports activity with their ex-girlfriend. And yet if he was doing those things with a male they'd have no problem with it.
Technically if it's a "platonic relationship" it's the same!
If a woman/man is "in love" with their current mate and they are forced to choose between their friendship with their "platonic ex" and "the love of their life".... lets just say love usually wins.