My Answer:
Well, it is not only the content management system or blogging platform that will bring you traffic. However, WordPress will make your posts have better links, and with the tagging and category links it will probably give you better ranking in the search engines. Also, everytime you post, WP will send notifications (pings) to search engines and blog trackers, which will notify them you have new content and give better ranking to your “fresh” content. If you have better ranking for terms that are searched often in the search engines, you will get more traffic. WP alone is not going to drive people to your site - the content of your site will do that - but if you’re asking me “is WordPress the best tool for me to use to make a search engine optimized site?” I would say yes. Definitely.

There are many factors in bringing your site traffic and keeping the traffic. This includes having great search engine ranking, having links to your site from reputable websites, having unique content that is valuable to your visitors, and creating a social buzz about your site through social media and bookmarking channels. WP can help you with these to various extents, but none of it is automated (at least not yet!). You need to get the links, make and promote the unique content, join and be active on the social networks, etc.

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Thanks to Taylor for the question.

Related: 11 Most Important WordPress Plugins to Build Traffic [FinancialJesus.com]