1) It sets up an expectation for the user that they are editing content on a page, as if they were editing a Word document. But they're not doing that. They're editing content in a system that then happens to be output on that page. It might also be output in other places on the site, maybe in different presentations. This causes weird spookiness-at-a-distance issues where making a change in one places has unintended consequences in another. Essentially you're presenting a metaphor of editing content on a page, but the metaphor is a lie.
2) It encourages the user to think about how the content _looks_ not what the content _says_. This is the same fundamental issue with WYSIWYG editors, where the user wants to make things big and red and underlined. And blinking. The role of a CMS user is to create content. The role of the web designer is to set up the system to publish that content in a way that communicates best according to the site's objectives.
3) The way the page looks when someone is editing on a big screen isn't necessarily how it looks to all visitors to the site. Even saying "this is what your site looks like" is a massive oversimplification. It's not even straightforward to define what a 'page' is on a modern site, and that's only going to get more complex as the web evolves. Trying to tangle your editing interface in with an ever increasingly complex presentation layer is setting the user up for a world of hurt. And lies. Hurt and lies.
It's simply not sustainable, nor a good idea to try to combine your content management and your presentation layer.