her kit does NOT fit the support better.
Bot lane has 2 players, your shield only shields one = better in solo lane (mid or top).
Your passive is spell vamp (aka: healing based on damage your abilities do) = better in solo lanes where you either farm (do damage to minions with abilities) or trade (do damage to enemy champions with abilities) as opposed to bot lane.
And your W, high damage over time spell. Your rank 3 W will clear a caster minion wave. To give you an understanding of how mu.ch damage it does.. oriana needs to Q W Q to clear a wave when morgana can just W it.
Oh, and your R benefits for you keeping the leash on your enemy. Meaning, you have to stay in range and avoid dying while its active. Again, better in solo lane as you only receive damage from a single source, as opposed to 2 in the bot lane.
So, by this we can see that.
Her passive is for solo lane.
Her W is for solo lane.
Her E is for solo lane.
Her R is for solo lane.
That's more than half of her kit.
And regarding "mid being largy roam based". Did I mention a single W can clear caster minion waves at lv 3 W? (that's lv 5 morgana)
You can roam much easier than most mid champions because you clear waves super fast, and from range, and you don't need to be in lane by the time the minions die loool.
So, yes, Morgana is very good at roaming as well. And very good at ganking too.
You can just walk close to the enemy from behind them using your black shield on yourself, now they can't cc you and ult them. Wait for ult to end almost end and trow a W under the enemy, and after they got stunned land a snare.
She also has spell vamp, meaning, she will be on high hp when roaming.
The only reason morgana is mostly played bot lane is because she used to counter the meta. She was an anti meta pick.
Back when bot lane was: blitz, thresh, leona.
And this community has a large amount of sheep in it, and they can't think for themselves, so, they stick with their slave masters that played her support in lcs => MORGANA BEST IN SUPPORT ROLE!!!
Even when most of her abilities work better in solo lane.
edit:
meanwhile, downvoted to hell
meanwhile, support morgana has lower win ratio than mid morgana.
sry snowflakes, reality isn't on your side ;)