Why no "Website" type under schema.org/CreativeWork?

In Pinterest documention on Rich Pins [1] one finds this recommendation
(and variations on it):

"We suggest that you also include your site name using an Open Graph
og:site_name tag. Schema.org doesn't support a site name field."

This is indeed true.

Perhaps this item type was considered unnecessary because of a view that a
"website" is simply the top-level URL for any Thing.

But as a creative work a website is not a URL, but a collection of URLs -
just as the creative work that is a book is not a page, but a collection of
pages.  And while such a type might engender confusion with other resource
types with which it is associated, like WebPage, websites obviously exist
as actual things out there in the world.  Just as a Book, or Photograph, or
Movie may be referred to representationally in web content, so are websites.

And while a website could also be thought of as the URL (as in the "url"
property) of an organization (as in the "Organization" item type), a
website can on one hand have more than owner, and the other hand an
organization can own more than one website - each with its own URL, name,
etc.

E.g., two Microsoft websites:

url:  http://support.microsoft.com/
name:  Microsoft Support

url:  http://careers.microsoft.com/
name:  Microsoft Careers

In terms of the sort of site name declaration to which Pinterest makes
reference (a ready-made use case for the utility of a website item type)
Open Graph - with its <meta> tag declaration method - is obviously not
constrained by schema.org's stricture that "you should mark up only the
content that is visible to people who visit the web page." [2]

However, virtually every website ever constructed has a "home" link
anchored either on text or an image which already declares the website URL,
with the website name at least strongly implied.  It wouldn't seem like
much of stretch to declare a website name here with a <meta> tag.

Image link, without schema.org markup:
<a href="http://example.com"><img src="/example-logo.png" alt="Example"></a>

Image link, without schema.org/Website markup:
<span itemscope itemtype="http://schema.org/Website">
<a href="http://example.com" itemprop="url"><img src="/example-logo.png"
alt="Example" itemprop="image"></a>
<meta itemprop="name" content="Example">
</div>

Such usage would, I think, fall squarely into the realm schema.org's
allowance for "missing/implicit information", where "a web page has
information that would be valuable to mark up, but the information can't be
marked up because of the way it appears on the page." [3]

I keep think I'm overlooking some principle that would preclude website
from being included in the CreativeWork schema, but I can't think of what
that principle would be.

[1] https://developers.pinterest.com/rich_pins/
[2] http://schema.org/docs/gs.html#schemaorg_expected
[3] http://schema.org/docs/gs.html#advanced_missing