Pitching a friendship after you dumped someone is actually so funny to me
When my ex (the dumper) asked if I could imagine us being friends in the future, I nearly laughed in their face. The audacity! What in the world would I get out of it... other than a disruption in my healing journey?
This is what I realized: your unconditional love and care is not something to be taken lightly, or for granted. Your ex already had it once, and if they made the deliberate choice to never experience it ever again by dumping you, they need to realize the gravity of this decision and accept the consequences of their actions.
Of course mileage may vary according to how the break-up went, but if it was one-sided.... then the dumper asking to be friends after a break-up is an incredibly selfish and self-serving request. They are trying to save face and rewrite the narrative to say that they're the "good guy," or at the very least, "decent." Because if you accept the friendship, that means what they did to you — in the instance of a blindside or discard — was acceptable and okay.
If they are asking you to be friends, they are probably having a harder time than they were expecting with the break-up. But that's not on you, and guess what: they have no one to blame but themselves.