First of all, it is productive. As a writer its important that you write as daily as possible, and I find that since starting a blog I am certainly writing a lot more. Even if it isn't a creative piece, sometimes it is good to just write whatever comes to mind, then at least I am filling my daily writing quota. It may be a load of junk one day and a heart felt piece the next, either way I am writing and hopefully becoming better at it.
Portfolio? I have found that having a blog is a really good place to display your work, it is good to have all your things in one place instead of searching through hundreds of different documents or diaries. Having a blog you can post all the work you're proud of. You are creating a portfolio almost, so in the future if you're ever asked about your work you can direct them to your blog instead of sending them tones of links, emails and what not.
It's fun. I genuinely look forward to updating my blog, it's good to share whatever I have. It also makes me feel proud in a way, even if no one reads it I know it's there and I can easily go and reflect on what I've written and in time I will see the improvement in myself. Plus I reckon in a couple of years times it will be quite amusing and sentimental to look back on.
I highly recommend everyone to start a blog, even if you're not a writer. You can display endless amounts of content on here,if it be your a photographer or I don't know a full time fan girl, you can write or post about whatever you please, it really is a good feeling have a blog.
