I disagree I am sorry but Twitter is a totally diffirent platform to your website for example

Say I ran an SEO Blog and I posted tips on that blog, Only people who knew the blog is there would see it but.

On my Twitter account say I have 1000 people following me and I post the link thats 1000 potential new customers and 1000 potential new people clicking my site which increases traffic and SEO.

I do agree though there is no point having a twitter update box on your website saying the last 5 things you put on Twitter as people already know cus they are on your website.