With the versatility that Morgana's kit offers i believe that her Q needs a smaller hitbox kind of like the mundo treatment a few patches ago. That is a really wide hit box for a 3 second snare not to even mention her follow up opportunities. I just think that there should be more of an incentive to hit the Binding instead of just throwing it and hoping it lands.
I agree with Rhyto, 
Q is very fast and there for has a small hit bot. The 
Q hit box is fine. In fact it is large enough that minions seem to always get hit when I play her
You have a point but of course as a Morgana Main myself it can be an issue because of her Qs slow speed players are able to avoid it from afar of course. Your positioning is really the key because all you need is a minion and you shouldn't worry about Morgana's W pool so much because it doesn't deal quite a lot of dmg as her Q does with 90% AP. Her kit is fine we just need to get used to laning with or against her in general.
It's the reason she's a support, in my view. Like Blitzhook, it's an ability that renders the target vulnerable for an extended duration. And spells like that are always better the more people you have to follow up. So the spell is enough to push her into the support role. Weaken the already unreliable spell much more, and she'll be pushed back into being an out-of-meta midlaner.
While I agree the duration of the root (it's a root, not a snare) is high, especially at low ranks, it is needed because of its high hit box and low projectile speed. It's a line nuke, nice heal for Morgana, and great CC allowing her and her allies to make a great advance onto a target that is hit, however, the spell if fairly unreliable because of its disadvantages. All and all, I think Riot needs to bring down the early root duration, keeping everything the same and allowing the spell to be 3 seconds at max rank.
No doubt that catching someone out with a Morgana Q is great for the team, but her Q is one of the slowest skill shots in the game and can be blocked by minions. She, by herself, can't always follow up on it either, particularly without her ult. It's honestly pretty fair to dodge; it might need an early game nerf, but nothing too big. Her spell shield is the main source of her power really, as it offers invaluable safety against the popular supports right now.
(I regularly play with a Morgana mid main, I don't know if that makes me an expert or not, but I figured it means I know her decently well.)
Another factor to consider is she is considered a mage in riot's eyes more than a support, kinda like 
. Without that long root she has no damage output. Her pool does a surprising amount of damage especially if they are already hurt, but it requires them to stand on it which is what binding was designed to be used for. In order to nerf the binding they would probably have to rework her pool or maybe the whole champ as well. My 2 cents anyways.
