Taking mid lane isn't about them not touching your turret, its about the relevant champion getting the farm and leveling they need. In most cases, you want the carry to be mid or solo lane.
Morgana is one of the best against other mages, because of her shield preventing any harass damage, and also blocking CC so it also means you will never get ganked. On top of all that, she has one of the best farming skills in the game, meaning you can constantly damage their turret.
However, Morgana falls down against AD carries. I think Ashe is still one of the strongest, especially once she hits level 6, because it essentially means you can't go near her turret without risking getting frozen by her ult and killed. Not only that, but she can use her ult to help her team in the other lanes, and she has an amazing scouting ability that makes sure she never gets ganked.