I like that idea too - using your LinkedIn profile as the home for your personal brand.
My only concern is that LinkedIn is a free service. What if they go out of business or decide to go in a different direction? What if some weird thing happens and your account disappears, and it takes weeks to get someone in customer service to help you (because you're not paying anything and thus are a lower priority than their paying customers)?
I love social media, but there's something to be said for owning your own piece of real estate - in this case, www.yourname.com and your own website.
Would love to hear others' perspective on this -