I personally don't see why it would be worse after a break-up than it is with step-parents. I know a bunch of people who had relationships with a single parent (who usually had a baby or a toddler), helped raise the kid, became a parental figure for the kid, and then when the relationship ended had zero right on the kid because they never adopted them or married the single parent and there were no blood links.
I personally think it doesn't matter who produce the genetic material of a kid. I don't expect any kind I ever have to be biologically related to me. Maybe they'll be adopted, maybe they'll be metamours' kids. While I might lose contact with them if things go wrong, that's true of biological kids too (especially if you're male) and people have kids anyways. I think the most important parts are loving the child and giving them a voice. If they grow up a bit and want to see their former co-parents again, even if they're your ex, I think they have that right.