Name-changer here too, as I don't want anyone in RL to work out who anyone involved is!
All I want to say is that many of you obviously have good reasons for cutting your parents out of your lives. However, there are two sides to the story. Two of my DH's adult children have done this to him. He is heartbroken, and has no idea why they have done it.
He is the first to admit that he wasn't a great husband first time round; he and his ex-wife married without loving one another, as they were both afraid of not finding anyone else. They did a good job of staying together until the children were 15, 18, and 20, whereupon they divorced. By that point my DH had already started a relationship with someone else.
As I say, he was not a great husband (I would have left him if he were like that with me!). However, he was - so far as I am aware - a good and loving father, who doted on his children. The third child would agree with this. She, for her part, is in the awkward position of trying to have successful relationships with everyone in the family.
My DH has three grandchildren whom he's never set eyes on, even in photos. It is a source of constant sadness to him that he won't ever know them. I find it deeply sad that these children will grow up without knowing their grandfather (and our children). I have no idea how this will be explained to them once they start asking.
If your parent was neglectful, abusive, cruel, an alcoholic/drug addict - anything like that! - I can understand the idea of cutting them out of your life without further ado. But if it's something more subtle that could be talked about - which would at least give everyone a chance to make things better for the future generation - I could only urge you to do so.