Well I dunno, honestly Cass has great AP, and if you run seraph's (good build? :
), she has decent health for a squishy mage, and her ap rivals veigars. She can close in on 1k ap quicker than he can - except veigar's ap keeps rising, so in the end he beats her. Honestly Cass lacks an escape. I don't know why she's so slow, I have a snake, and he's a really fast guy.
I mean yeah, not all assassins focus, the idea is that there's variety of course.
Cassiopeia aside, there's lots of strategies to counter champs, but like I said, movesets for assassins I think are innately better. What use is health to sustain you, if you cant hit your opponent?
Anyway I say this because most of the time I see an assassin vs a mage, the assassin wins most of the time (greater than 50%, not going to bother getting specific about the math). Assassins are good, and common in mid lane. I think there are a few that are good vs them though, like brand, and annie i've seen counter fizz. She usually waits for his jumps, then stuns him and bursts him down.
Morgana is too difficult to say. A good morg CAN, but if she doesn't land her q she cant do much besides nerf your ap with her shield.
While some mages do better than others, the reason it seems one sided in general is assassins are suppose to destroy isolated squishy targets 1v1. Mages tend to be more team fight oriented. To really beat an assassin in lane easily, you would want some tank or fighter with good early damage and survivability like Renekton (a good counter to Zed in lane).
Mages can win, they just have far less room for error.
Here is the best replay I have on hand for showing what I mean: http://www.lolking.net/replay/na/1613952367
(Not an ideal example, as the Kat player does not really use her in ranked that much though)
I bring up Morgana because that is the mid laner I am working on at the moment. Ahri is my preferred champion for going up against Fizz and Akali at the moment because she is the one I have done those match ups a lot with.