I started to read your post and thought "Nooooooooo!"
My ex (The one who recently passed) contacted me some weeks after breakup with the "we should still be friends" mantra. We went out to lunch. Over our meal, he said he had to apologize. Then he told me (I'm laughing now, 'cause I can't believe the gall) he was sorry about our sex life, because Susie had relieved him of his inhibitions and he realized how much better it could have been.
You can't make this stuff up.
I've long thought the "we should stay friends" gambit was more
PR to prove "I'm still really nice...look, I'm still friends with the person I ended the the relationship with."
I know exactly one person - one - who is friendly with the man who told her he no longer wanted to be married. She actually thanked him for helping her through her cancer treatment.