The problem isn't Morgana herself. I think Morgana is a good champion, she one of the only champ that isn't overloaded and her black shield is needed in this meta where one CC and with all the dmg, you can die easily.
But ofc, if you play 
, 
, 
against her, you are not going to like it. The problem would be counterplay. Yes Morgana can make the horrible opressive Leona useless and that why we like her. Because what can you really do vs Leona besides staying under turret ? Her combo is a death sentence. Morgana is one of the only supports that can resist to Leona because her black shield make the red hair kit useless since she won't CC anymore.
Especially when your adc isn't good. You can't save a bad Jhin or a bad Vayne from a Leona combo with a simple shield. You need to nullify thoses CC.
That why i like Morgana. Most of the time, she will be the only support that you can pick to save your adc from these champs who can hard engage your adc. When your adc don't know how to position, how to play safe... Why should i pick 
or 
? I know it's won't be enough to save him. If i can have a special shield that can save him from any engage, then it's will be easier to not lose the lane.
But when she is paired with champs like 
or 
, yes she becomes a problem because she erases the weaknesses of these champs. Yi may be weak but if you can't CC him, you can't beat him. With Morgana shield, he become a monster no matter how much CC your team have.
The same thing goes on for Katarina but the only difference would be that Katarina needs skills and is harder to play (sorry for Yi mains but honestly timing Q is not that hard). Also Katarina kit don't allow her to be untargetable like Yi Q. So Yi can dogde a lot of spells before the blackshield stop them. This duo reduce Yi counterplay to "not feed him" and "destroy him in early in his jungle" which isn't simple to do because not feeding a champ that is really fast at killing you while being impossible to CC is almost impossible and destroying him in early mean that your jungler must have a good early champ for stomping him and you also need to have advantages in lanes because if top lane isn't pushed, if mid isn't pushed or if bot isn't pushed, then you can invade Yi but his teammates are likely to react and kill your jungler.
I think Morgana depends on the situation. Sometimes she can really be oppressing because yes, being countered by a Morgana isn't fun at all, watching a Yi Morgana combo destroying your team isn't fun too but don't forget that playing vs champs like isn't fun too and nobody likes to be engaged at lvl 3 and die because Leona just landed a E, a Q and a W with her adc barely following her.
Nobody likes to be countered to the point of being useless. It's the same thing when you play 
vs 
on top and she can makes the entire Irelia kit useless being blocking a Q reset with her W. Or when you play 
and you lane vs 
who can W your E.
Your problem isn't Morgana, it's counterpicks. Some champs beat some others without doing a lot of efforts. Poppy for example. You time your W correctly and Irelia is dead because Irelia is useless if she can't perma dash with her Q. It's doesn't require a lot of skill to do.
Morgana is in the same case. You press E on your adc and Leona is useless. Then you CC her with your cage and you walk away... It's doesn't need a lot of efforts.
Counterpicks are horrible ofc, but this problem will only grow bigger every years because more champs mean more spells and more spells mean more chances to have something that make a champ useless.
's AOE root