nav > ul is sometimes redundant

Does the following note also apply to headers?

*Note:* Not all groups of links on a page need to be in a nav element — the
> element is primarily intended for sections that consist of major navigation
> blocks. In particular, it is common for footers to have a short list of
> links to various pages of a site, such as the terms of service, the home
> page, and a copyright page. The footer element alone is sufficient for
> such cases; while a nav element can be used in such cases, it is usually
> unnecessary.


For example, inside the header element, I want to do:

<nav>
  <ul>
    <li><a href="/">Home</a></li>
    <li><a href="/about">About</a></li>
    <li><a href="/contact">Contact</a></li>
  </ul>
</nav>

Why do I need the extra nav element? Wouldn't it be simpler if I could
remove the nav element and perhaps replace the ul element with an nl
element?

References:

http://www.w3.org/html/wg/drafts/html/master/semantics.html#the-nav-element
https://css-tricks.com/navigation-in-lists-to-be-or-not-to-be/