Yeah, Morgana mid isn't that strong alone. I'm sure this will be downvoted by silver players, but it's the truth.
Morgana thrives by shoving wave and coordinating with the jungle. Get an early game jungler like xin or udyr on your team and you will roll over mid lane or roam and roll over every other lane.
Morgana's 1v1 kills generally fall into two categories:
1.) The enemy foolishly tried to all in you and got bound in a creep wave or otherwise awkward position leading to his death.
2.) You flash ulted the enemy immobile champion.
She has zero kill pressure 1v1 against intelligent opponents. Literally zero.
Here is how I play Morgana mid:
I safe farm until first back. Buy boots and a lost chapter. I shove the wave and roam bot repeatedly. Alternatively, I ping my jungle to come mid and we 2v1 the mid and kill them repeatedly. This playstyle is pretty much identical to any other roaming champion mid.
So how do you counter this if you're playing against Morgana?
1.) If you're a mage you can easily match Morgana's shove. You need to take dematerilizers and shove her into the tower so she can't roam. If you're against an early game jungler you should take cleanse and ward intelligently.
2.) If you're an assassin you sit mid and farm. You wait for her to back and look for picks on her teammates. If you're Zed and you get even a single kill you should be able to solo kill Morgana, but again be careful if she has early game jungle help.
One thing people need to get over is the incessant need to kill. It is possible to out farm Morgana mid and scale. Just because you probably won't kill her in lane doesn't mean you can't win the lane.
By the way, shoving Morgana early fucks her hard. She CANNOT cs under the tower. It is hard as shit. Shove her level 1 and 2 and you will put her behind in cs pretty easily.