I could have written a long letter to my father telling him that I hated his addiction, wanted him to find recovery, and that I love him.
He would have looked at it, shrugged, and walked away.
No impact.
He was one of those driven functioning alcoholics who, by the miracle of denial, are absolutely certain that their drinking hasn't harmed anyone and that all those nights of screaming hate and contempt at his family will just be forgotten like a hangnail.
Your letter is valuable for you. You have gotten your feelings out on paper and have shown us exactly what you think about your relationship with your father. That kind of 'spelling it out' is very important for you.
Just don't be surprised if it produces no reaction from your father - zero, zilch - or just a heap of denial.
Set up boundaries so that his insanity will not affect you anymore, and let him know that you are there for him when he decides, as in real actions not promises, to take the path of recovery.