I think this is a great proposal - I haven't gotten very far in the beta myself, so I can't comment on on if +4AP would be too harsh a penalty, but if this were to be the case I would suggest having a talent that would remove 1 AP spell cost (applied to penalties only), with the prerequisite of having 2 points in 3 different spell schools. For those of you who have played Master of Magic, it would be similar to the requirements for Node Mastery, which was an amazing trait to have but really only applicable to specific builds.
I do agree that whether or not you can learn a spell should be dependent on intelligence, but spell effectiveness should be a combination of intelligence and skill level. There should be stiffer penalties in place to prevent the jack of all trades mage, but still make it somewhat viable for a unique playstyle - you won't be the most powerful mage for each school, but you will be versatile.