Cookies are used to store session data when you leave a site so it can be restored when you return.
If you stay on a site, that information is part of the session and not a cookie.
I have read on many sites like arstechnica that cookies can invade my privacy
A garden hose can be used for a surprise colonoscopy but that is no reason not to have a garden hose.
The idea that cookies can invade privacy is a silly one, not because it's entirely untrue but because it is such a minor thing compared to the more prevalent methods. Advertisers do track users across websites but they don't do it by using cookies, they do it by saving that information in their database. Things like Google analytics or Google adsense for example are on so many websites that it can basically track you across the web. It can see you on "BobsFarmingBlog.com" and "PaulsTractorCorp.net" and similar related sites and save that information on a server side database, then classify that you might be interested in a new tractor and show you ads for tractors and farm equipment. This behaviour is not related to cookies.
Some of these advertising widgets/components do save cookies. For what purpose, I don't know, since they can't really get more information from you with them. You can block third-party cookies pretty easily though with most web browsers- for example on BobsFarmingBlog.com, BobsFarmingBlog.com can save cookies, but ads.google.com cannot. ads.google.com will still save your IP address and what website you are viewing and your browser fingerprint into it's massive database, but hey at least you won't have a scary textfile connected to your browser.