The default login form is not very developer friendly (and it is more developer friendly now than it used to be). If you browse the source for that page you should be able to convince yourself of that.
Your plugin is not going to be able to manipulate the page the way you hope. A theme could create its own login page, but even that doesn’t actually eliminate the default page.
You could attempt to circumvent the login page and replace it via something as in this answer but as stated in that answer it seems prone to error as wp-login.php is hard-coded into Core source multiple times.