There are a couple of problems with using the “public” pattern:
First, you can’t “drop in” and install the way you currently can with Omeka, as the benefits of that system only work if you’re controlling where the DocumentRoot is (speaking in Apache terms).
Second, we need more than just index.php to be served, in particular static assets must also be served. For the core we could move the assets directory under that same public/ tree, but modules have their own static assets: there would have to be a system were that stuff is copied under public/ when installing or updating a module. A similar situation applies for themes.
I’m not opposed to the idea on principle but it does raise some issues.