I will keep this short. No use me rambling, which I could.
Besides the fun derived, I write because it is the most educational discipline I have ever undertaken. Now, that is a powerful statement, because I spent the better part of my working years as a professional musician.
As a result, I know the meaning of cultivation, investing many hours to discover that many more hours are needed.
Since I have always found learning enjoyable, and since writing requires a constant stream of it, writing improves my knowledge and my intelligence.
Now, I am not saying that I have more knowledge and more intelligence than anybody. All I am saying is that writing helps me in those respects, and to me nothing is more frustrating than stasis. Thus, I write to keep growing. And to grow is fun. And what is more fun than fun?
The answer, of course, is more fun.
Writing is brain food. Growth is fun. So writing is fun!
Of course, I could list multitudinous other benefits. Why bother? I have listed the most important ones without rambling.