I had a major falling out with my father after my baby was born, he just wasn’t that bothered and some other things happened in the family that put a lot of strain on the relationship. We ended up no contact for a few years, not long after a similar conversation to yours, his choice to blank me although he blames me and there was/is hurt on both sides. Our situations aren’t the same but you may end up where I am in the long run. I’ve realised my dad doesn’t have it in him to be a great or even average dad/grandad.
My mother managed his behaviour when she was alive (e.g. remembering our birthdays, congratulating us for important things) and I didn’t realise how much of a role she played until she was gone.
I have now reconciled to the fact that he cannot be the father I want him to be. He will let me down. He shows very little interest in me or my son and concentrates his energy on his new wife. They recently recounted joyfully how lovely it was to have (her) grandkids jump into bed with them when staying over with her daughter recently. That sort of thing used to be a lot harder for me to hear. It took a long time for me to come to terms with who he is with but maybe it’s where you have to get to? The old thing of when people show you who they are, believe them? He may not change.
Like you, I live far away and he makes no effort to visit. He has not been to my new house - I’ve lived there for 6 years. He has had multiple holidays to see his new wife’s family and they live abroad.
I have learned to really value the people who make an effort for me, be they friends or family, when you think about things clearly you can determine who the really good people in your life are and they are the people you need to spend your energy on. I often go ‘back home’ but never stay with my dad, we as a family go to an old school friend who is now like an aunt to my boy. It works out better for all. My dad would make it an unhappy experience if we stayed, my friend loves us coming, we fill her home and we all have a great time, we all choose to spend Christmas and holidays together these days. We share a lot of love and care. One door closed when my son was born and others, particularly this one, opened.
In answer to your question, I would say to you, don’t cut ties, but learn to care less and put in something close to what you get out. If he doesn’t call at the right time, don’t answer, if he doesn’t visit, so what. Expect less, spend energy on those who do care for you and your child. Move on and leave him behind if that is where he wants to be, you can’t force him to be what you think he should be and trying to will make you both unhappy.