Can a business make a case for ordering the removal of photos tagged to coordinates on its property?

Your idea does not sound viable.  For certain famous privately owned properties, they can prevent other photos from being published.  For everything else, normal photography law applies: In the US (and I think in Western countries in general), you are allowed to photograph any place, thing, or person in public, especially when taken from a public place.  You can't invade privacy into a house with a zoom lens.  You can't use a picture of someone commercially (i.e. in an ad or similar) without their permission, but you can use pictures of anyone editorially (in a newsworthy article, discussion, critique, or privately).