In most places in LinkedIn you won’t see a URL on your Professional Headline become a hyperlink.
But there is one very cool place that it becomes a link: In my email inbox. Look at this:
This is what I see in my inbox this morning. It is the daily email I get from one of the Groups I am following.
These are Discussions, new and old. It shows the title of the Discussion, who contributed (the name), and then the Professional Headline.
The arrows are pointing to the hyperlinks.
This is profoundly powerful. This means that if you are active in a Group Discussion, when others see your contributions in their email inbox, they have an easy one-click chance to go to your website.