1, we would have to set up a global registry for SSIDs, like we have for domain names. (Otherwise, what's to keep someone else from using a colliding or misleading name and getting a certificate for it?) And even then you run into the problem that the CA infrastructure used for the web is pretty terrible.

2, clients would need some kind of policy database to know what kinds of traffic must go over a "secured" AP and what kinds, if any, can go over the local coffeeshop's or convention hotel's wifi.

And all of this to secure just one link of the communication— all the rest remain vulnerable. Really what we want is end-to-end encryption, not link-by-link encryption. If you have #2, for example, you could instead use that policy database to implement mandatory IPsec (or equivalent end-to-end encryption; MinimaLT if you prefer) for all sensitive traffic, and bingo, you're secure against whole classes of attack even when you are using unknown APs.