What is dofollow and nofollow?
 

I completely agree with your point that no follow links does not play any role in ranking where as do follow links share the page rank and also count as quality backlinks.

When Google bots are crawling a website they look for external links point to other websites. If this links is “do follow” then search engines will follows the link and so link juice gets passed. While If a search engine finds a “no follow” backlink it will just ignore the link and will not get deeper into crawling and no link juice is passed.