I have never built a site that way myself, but I have rebuilt a couple that were. I was specifically asked to rebuild a site that had been built in this manner because the client found it cumbersome to use. Because everything was a post just divided up by categories they had to click posts and then select the appropriate category to see the posts they were interested in.
When creating posts if they forgot to set the category, the post didn't show up anywhere on the site because all archives were generated by category. Easy enough fix once they caught it, but why bother? I don't think this is easier for a webmaster really more of a pain.
With a little training on wordpress, my clients have always appreciated the fact that when they want to post to their blog, they click "posts" and when they want to add a page to the website they click "pages." In fact, I use custom post types to handle different types of entries for my clients because that breaks it down even further for my clients and they prefer that. An example would be creating a custom post type for "properties" for a property management company. But what exactly do you mean by "routine edits"? I think of routine edits as updating telephone numbers, addresses, etc which I would think you would handle with widgets in any event.
I am not sure what you mean by "less files." As all entries whether posts, pages, custom post type, etc are stored to the posts table in wordpress there are no more or less files or tables based upon how you enter the information into wordpress. So, unless I am missing something or misunderstood your comment, there is no benefit there.
From an SEO perspective, using the structure that is built into wordpress should again be a benefit. For example the Yoast SEO plugin allows for you to template your meta titles based upon post type (page or post), although manually setting them is always best. The permalink structure allows you to have dates shown for posts, but leave them out for pages and other post types. So the added flexibility of uses posts, pages & other post types is a benefit for SEO as well.
Finally, since Google is believed to use categories and tags to determine what the content is about, you are probably losing out on a opportunity for SEO benefit by using them for site architecture.
Honestly, I think using categories to set the architecture of the site is a throwback to when wordpress was much less robust than it is now. It was a workaround to be able to divide information up in a logically fashion on a site when you had no other options. Now we do.
Good luck!