Yes, I agree with you... More popularity, more socialization....more inquiry especially for the new products or offers you want to promote.
Whats the point of that ? Every Twitter link is no follow ? Any links you give to Twitter just promotes their site, thats why all the pages have amazing pr, because they are hoarding all the link juice and keeping it to themselves, this was NOT how google intended the use of no follow, all the big sites are at it, digg, wordpress, wet paint
Twitter is good for web traffic if you do it correctly. It can also fetch link to your site. Just promote your twitter account page
What you need to do if you are, say, SEO business is Tweet special offers and deals plus you can add links to coupons and let everyone know NOW what you are offering services.