I believe that you can get rid of tags and archives in most situations. However, good use can often be made of categories, author and pagination.
Let's imagine that you have a website or a blog (there is no difference) about "Widgets". Every time you find a new widget you photograph it and write a post with substantive content about it. You are a widget expert and know an awful lot about them. Widgets are a popular collectable and lots of people are interested in them. So you start your blog (or website) and publish posts (or pages) about two or three different widgets every week.
You realize that there are different types of widgets based upon what they are made from and everybody knows about this. Lots of people search for wooden widgets, brass widgets, copper widgets, plastic widgets,etc. So you make these the categories of your blog (or website) and all of the post about wooden widgets are posted to the "wooden widgets" category page. Same for "copper widgets" and "brass widgets" etc.
Your post pages display the full size photo and everything that you had to say about that widget. Your category pages display a small photo of the widget and the first paragraph of your article. Soon, you have posts about 10 brass widgets, 12 wooden widgets, and 22 plastic widgets and those category pages are starting to look healthy. They might start ranking for in the SERPs for keywords like "plastic widgets" and "brass widgets" and pull in more traffic than all of your posts combined.
After you have about 20 post showing on a category page you might start using pagination to keep that category page from being enormous. Then when people read to the bottom they see a link for "earlier posts" and click it. That takes them to the older posts for this topic and you get more ad impressions. Now the pagination pages have become valuable.
Your author page might have some bio information about you, noting that you are the president of the Ohio Widget Collecting Society and are a professor of design at a college, where you teach a course on the History of Widgets in America. You can construct the author page to display your bio and credentials information at the top, your most recent ten posts below that, and your most popular posts below that. Author pages are valuable because people want to know about you. Google wants to know about you too because they want to determine if you are a credible author for "widgets".
From experience I can say that category pages can pull in a LOT of traffic, and a REALLY LOT of traffic if you rank well and the topic of your page is heavily searched. Your author page can help people to decide to link to you, invite you to speak at a convention, ask you to teach a course at a local university, Google might use information from your author page to decide that you deserve better rankings than other authors who post prattle about widgets. And, your pagination pages can make a lot of extra ad impressions.
So, carefully consider the potential category pages that fit your blog, try to find keywords that are logical fits, optimize those pages to rank for heavily searched queries. Wordpress gave you lots of options. Decide how you can use them in a planned way for visitors, searchers, and your own goals.
Good luck.