You can always use a static page for your home page, and put whatever you want on it.
And you can put whatever you want in your menu.
The category or date archive pages will still be accessible, but you don’t have to link to them. You can also use a plugin to change the rewrite rules so that the standard pages are not produced.
Many themes don’t put navigation links on the single post page (I never liked those). And especially if you just use Pages, not Posts, then there is no navigation, no dates, and no taxonomy pages.
The problem with this is that you can’t predict where the user will enter your site. Not everyone starts at the home page.
I experienced this just yesterday, when I read somewhere about a topic and searched Google, finding the site’s announcement category page. But it didn’t have links to the home or all of its own pages (including the first announcement which only showed an excerpt), since the other article referenced something about finding related software at their site. So I was unable to find what they said was there (no search either). It was very frustrating.