Can WordPress comments have titles and taxonomy?

Well. Theoretically.

  1. Comments do not have title field in a database. However they have meta natively, so quick add_comment_meta() can get you title–like custom field.
  2. Comments have links (get_comment_link()), but they are heavily based on context of singular post displaying them. Displaying comments by themselves with their own URLs structure would take some creative rewrite effort.
  3. I can’t say about level of effort it would take for taxonomies to work with comments, but it’s definitely not a natively supported object type for them.

In a nutshell you are going to be trying pretty hard to make comments behave like a custom post type and they just aren’t that. Although it would make sense, but WordPress, backwards compatibility, etc.