I have a lot of thoughts on this topic. I guess I consider myself a writer, and up until five weeks ago I was also a heavy drinker.
I see your point, I have had the same thought at several times, but really it only looks good from a distance. If you take those great drinker-writers, how many of them were able to keep up the creativity into their late lives, even if they continued to drink. Look at Hemingway. The guy basically destroyed himself psychologically over the idea that he couldn't write anymore. He wrote a great book about it, The Old Man and the Sea, and then he shot himself. Long term alcoholism will shatter you outright. Hunter Thompson, another alcoholic, is a writer and humorist that i greatly respect, but take a look at how he turned out in his later years. There is a video on Youtube with Hunter on Conan, it's pretty sad from a big time Hunter fan's perspective. Also, look where he ended up, same place as Hemingway, with a bullet to the head.
My point is that it probably isn't quitting drinking that makes people lose their talent for writing, not entirely at least, and long term alcoholism will have just as bad an effect, if not much worse.
Mix some alcohol or drugs with a youthful fire and you can get some explosive creativity, but fast forward forty years down the line and you just have a bloated shattered and pickled mind.