I understand why you would think that but then that would cripple Annie all together. Oddly enough it would probably even change her difficulty up a notch. Heck her kit would probably need a change accordingly to the stun change.
It would make anything Annie related a completely timed play. Aslo. Annie isn't a support, using her as a support is like using anyone else that does damage as a support. I go Katarina and elise support from time to time. Along with evylen and Yorick. And they too can already solo a ADC as well. Don't you think this the point to doing so in the first place?
Maybe this would be a better way of showing what I mean. Making Annie's Stun timed would kill her in lane when not randomly using her as a support. When she is in her own lane (gods forbid) even jungle. Lets say you proc her stun for a gank or for a situation about to come to you. Annie mostly relies on her stun. So once that is gone she is going to have huge problems. her gank becomes pointless besides showing up and scaring people away, or she is now in danger because her stun was waited out so the enemy team can do as they please with her knowing she can't get her stun back for at least another 15-26 seconds (if she is not willing to sacrifice her ult for that extra stack on her q or W stun).
I hope this helped to show what I mean?