1) Support doesn't need to go mid to cover their warding duties. While support has access to top river for warding, there's no point warding Baron during the laning phase because no one is strong enough to take him. In fact, they're welcome to try! Whereas Dragon IS up for grabs. So Support doesn't need to have access to top. Warding baron at level 6? Why!?
2) You don't send AP mid because they're AP. You send them mid because either you want to leverage someone with strong mid-game scaling (either by early-mid burst like LeBlanc, or by a strong ult like Pantheon or Karthus) in the position where they have the best access to top and bottom lane ganks...... OR.... you're running a champion explicitly designed to counter such a champion (Kassadin, Talon, etc.) It has nothing to do with 'AP carry' per se... it has everything to do with 'Does this champion have mid-game potential to wreck other lanes.' Pantheon goes mid, not top, because you want his ult to reach all lanes, not just mid.
3) You want two players laning close to baron, so while this reason alone makes mid or bot viable for a duo lane. However....
4) AD carry has the strongest -late game- power. Unless he gets fed, he's not going to be able to roam around and gank with impunity. That means he's unable to leverage mid's advantages in the same way that your standard mids can. So there's no -reason- to put him mid unless you're doing so as a counterpick against a champion that CAN leverage mid. But in those cases, you still won't duo lane mid, because such counterpicks need to scale quickly and having someone there splitting xp doesn't get them their skills quickly.