I played Vayne in the mid last night against Karthus (our Kog'maw didn't want to go mid). I did much better than I thought I would and forced Karth to zone out several times. I was able to consistently double-hit Karth and when their jungler came around, I used Condemn to get space, Final Hour and Tumble to get away.

It's the first time I played Vayne in the middle and it's quite likely I laned against a bad Karthus.

Well for one, supports are supports and cannot support unless they have someone to support. Get the idea?

well, bot lane is harder to gank than mid, giving protection, mid is easier to acsess bot and top so the hypercarry dmg should obvs be solo mid and have the most awareness+presence?

To answer the OP's question.

Like others have said, the side lanes are harder to gank than the mid lane. Therefore, you put the character with the best escapes there. Also as others have said, whether you are purple or blue, you would like to have the character that benefits most from blue buff be in the mid lane so that whether you want to take theirs or yours, that character is close by. And so, the AP based character will go solo mid because...

a) they generally fit the requirements outlined above (those that don't aren't seen very often)

b) they work better off of experience than off of gold (as compared to an AD carry) and so they can afford to ward themselves and not have a babysitter do it for them

Hope that helps!

It doesn't work because your ganks from mid stink.

While it is much more common to have an AP champion mid, I do tend to see a fair number of Ranged DPS Carries like Caitlyn and Tristana. Occaisionally I will see a Twisted Fate or Ezreal, however they are not as common as the fomer two. Also, I have seen (albeit few) successful supports mid. Most often I see Zilean or Sona mid, however on occaision I have played Galio as a support tank and completely destroyed mid. (For those who dont know, Galio's passive makes half of his Magic Resist into AP, so building MR makes you stronger, as well as have a better defence for the typical burst caster mid.)