Hey There
Categories can certainly bring traffic, so I typically do index them. (I do recommended noindexing subpages of archives though - page 2 and onward etc).
But if your goal is to target more keywords, these are typically best done with creating new posts or pages around them, if they are unique enough to warrant new content. It's best to keep your categories to a minimum (7-10 maybe top level categories - you can nest more under those if you have to) - but design your categories for best information architecture. Let your posts and pages carry more keywords.
I would not recommend trying anything as an SEO "trick" like using the canonical on pages that are different keywords. The canonical is only for pages that have nearly identical content.
Hope that helps!
-Dan