One thing you did by getting rid of tags, categories, and possibly 'a few other frills' is you demolished a huge internal linking structure that existed on your

One thing you did by getting rid of tags, categories, and possibly 'a few other frills' is you demolished a huge internal linking structure that existed on your page. Just like every external link pointing to your site gives you 'link juice' (I hate that term, but can't think of anything better right now), each internal link on your site passes that juice around. If you had a nav bar or widget pointing to your categories pages that then pointed to the posts in that category, that gives you tons of internal links. Also, having a large number of internal links shows the search engines that the site is well maintained. Getting rid of the majority of your internal links could certainly have this effect in the search engines.