Why won't my posts appear on the Static Page I select for my Blog?

I have been creating Wordpress themes for a couple of years and could never figure this one out.

In Settings-->Reading-->I select "Static Page" for Front Page...

My Front Page is set to "Home"
My Blog Page is set to "Blog", a page I created and it uses a template I created called "Blog". The template has the loop on it, but it doesn't seem to pick it up. I know it defaults to index.php or home.php in the Template Hierarchy...but why is there an option to set the template to on the edit page for the blog page if it doesn't pick it up? In other words, the code from my page-blog.php is ignored while it uses index.php or home.php's code instead. Thoughts? Or perhaps, I am missing something?