My biggest gripes with the mobile versions, app and website, are the lack of categories at the bottom of the page. It seems that there's been a de-emphasis of categories in general on Wikipedia. I hope they don't get rid of it though, because it's a fantastic way to organize related content. The contents of a category box often show relations between subjects better than the article itself
On the mobile site, go to the settings in the sidebar and enable Advanced Mode.
And no, they won't ever get rid of categories. It's just that the phone variants of the site are very heavily geared towards a specific type of reader, at the expense of editors or other types of users. They have been trying to address this over incremental updates though, such as now showing talk pages.
