(This is something that I wrote on a.wholelottanothing.org.)
I can see some people will only want tags OR categories, or neither, but there’s definitely a case for both. For example, on my mum’s site she uses categories for different kinds of post (articles, transcripts of interviews, lectures, etc) and tags for the topics each post is about.
On the old WP interface, if the browser’s wide enough, the Screen Options tab on the Post page lets you show/hide different elements of the form… Maybe that got omitted in the new interface (don’t get me started on helping people learn to use software that has more than one interface).
See on a.wholelottanothing.org.