Why doesn't Blog Post read my custom template but it reads the Main Side widget?

I have a page dedicated for blog posts.
I tried to use customized page.php template for it, basically to remove footer and header (just to test it out). I selected the template for the blog post but it doesn’t apply it. However when I add widgets on the Main Sidebar widget, it applies to the blog post.
I tried applying the page.php template to other pages and it works, just not this blog post page. Why is that?

Best,

RP