part of the reason you send bursty champs mid usually is because they can kill you before you can get back to the tower. The lane is shorter
The short lane also messes with how you farma and duel
Then there's the matter of ganks. Everyone can gank mid. Mid can gank mid. One does not simply go mid and expect just a few ganks. You are NOT freezing any lane in mid as fiora unless the other guy simply cannot unfreeze a lane fundamentally for whatever reason. Meaning they also made a bad mid pick. if you do manage to freeze a lane the jungler may just come dive you through a freaking wall because welcome to midlane biiiiiiiiiiiiiiiiiyatch
http://i.imgur.com/VLEySAM.gif
Then there's the matter of the midgame. Nobody cares if your lategame is cool, you need to carry midgame or the team needs to adjust to whatever it is you do actually do. Are you going to splitpush? What's gonna happen midgame then, what will top be doing? You can't just go splitpush and duel like fiora would normally do if you've got a tryndamere top unless he's gonna do it.. you need something here, what happens if you get sieged, fiora gonnna go wipe out the minions with her aoe sneeze? hell no. She doesn't have very good cc either. But she can do something if her team helps.
Over and over again no matter how you slice it, if you have fiora mid you are going to have to compensate for some stuff which isn't necessarily a deal breaker but you aren't gonna just gonna randomly pick fiora mid and expect anything good to happen after lane phase unless your opponents are bad or relying on something that is countered by something like fiora which isn't gonna be much, sure she can duel them but they aren't gonna duel you. Theyre going to vomit magic and walk away laughing over like 300 units to safety as opposed to the normal 1000 you see in top lane.
Also ganks work different in top and mid, you have some idea where the jungler will come from most of the time in top.
But then it goes further, one of your responsibilities is to defend the dragon. If you have to go do something about a team at dragon and end up having to try and stop something you will have no cc. You'll have to rely on someone else for peel if the situation arises or run away while you fail at your duty.
Then there's the whole AD mid thing... not just any team can afford to do this.
Theres probably other issues as well