I wrote a lot of letters. I began keeping them to myself because, like everyone says, alcoholics don't 'get' the letters any more then they get the words we've been saying until we are blue in the face. The letters were good for me to write though so I kept doing it - for just the reason you said. I wrote them to him but they were for me. In the end I began writing more to myself.
I think it is fine to give it to him, or read it to him, if it is going to bring *you* some closure to do so but protect yourself by exploring your expectations first. If your expectation is that this is going to somehow illicit a new response from him, you aren't going to get any closure.
I just started saying "I won't do marriage counseling until you are 6 months into recovery. That is a promise to do marriage counseling, not to stay married." Nothing more. I dug in my heels.
I said it over and over. Not even that worked. The divorce had been filed already and was on 'hold' after some threats from him. Still on and on and ON with the "I don't know what you want." in its various forms. So I got even simpler. "I no longer want to be married." Nothing after that. No more reasons or explanations. This he understood. He still didn't believe it (based on his words and actions) until about a week after he moved out. Acceptance (or at least the emails stopped coming) months after that.