A major reason why Wordpress is popular is because of excellent timing. It came out and solved a problem (easy Website content management for non-technical folks) in a revolutionary way. Its Famous 5-minute installation demonstrates that it is a tool created explicitly for the end-user, and this has always been its focus, and it started with this vision at a time when the normal process of updating a website involved hand-editing static HTML/PHP files, and a lot of manual work to upload to the production server via FTP. Wordpress wasn't the first to create a system where websites could be managed entirely from the web (in fact, it started just as a fork of the b2/cafelog CMS), but it did manage to come out at the right time and offer the best solution for this problem at that time.
As a tool for the end-user, they have continued to see great success all the way up until today. They created a for-profit company, Wordpress.com, where users can get set up with Wordpress without even needing to install it themselves. Users add plugins and themes from an easy-to-use marketplace, and because of the way Wordpress is set up internally, they all work together reasonably well. And because of its rich history and the prominence of the name "Wordpress", clients just want to use Wordpress, not other systems. Webmasters have been managing Wordpress sites for years, and they don't want to take the time to learn other systems, even if other systems (from a developer's perspective) seems like a much better match.
I have experimented with several other CMSs, and while there are some really great ones out there, the fact is that none of them really have an ecosystem large enough for a non-technical person to actually build the website they want. Wordpress is still really the only viable solution for a non-technical individual. The other CMSs that have seen great adoption all focus more on the developer than the end-user, which isn't a bad thing, but it does limit their usefulness to the broader population.
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