It shouldn't break any themes if done correctly.+Jason Schuller
I could see this being extremely useful for themes. It'd be a lot of work to implement something like this in core though. It'd require more than just removing admin menus as well. For example, assume a theme wanted to remove support for pages. Core would need to disable all functionality related to pages, including admin pages, nav menu items, and the pages widget.
There are also some things that a theme shouldn't have this type of control over. You mentioned "comments" above, so I'll use that as an example. Whether comments are supported is defined by the post type. For example, the "post" post type supports comments. Any theme that supports posts should support all post features, which would include comments. If a theme didn't want to support comments for posts, then it really shouldn't be supporting posts at all.