I can only speak from my own experience running various communities: hardly anyone likes to have their blog hosted on a forum site. There are some rare cases where a user will use the forum blog to post about forum-specific things, but the vast majority of people who are willing to blog at all have a blog of their own. It's disgustingly simple to sign up for blogger or wordpress.
Having a blog app on the forums is wonderful -- but no one uses it. They don't want to split up content between the forum and their own personal blog. The end result is, they ditch the forum blog and just continue to use their own.
But if posts could be syndicated from an external blog, like Amazon does (to great success I might add!), then we get the benefit of blogs even when users are using some other site. It adds just another feature for users to continue to come back and use the site.
I wrote a mod that did this for another forum software and the users LOVED it. It was a really well received feature. We started displaying "Last Blog Post" in the postbit which encouraged more posting (most of which was legitimate, not spam). The whole community saw a bump in participation.
People love to share their blogs, they just need an efficient way to do it. I'd rather syndicate posts and keep visitors on my own site, rather than have them click a link in a signature or something and leave my site.