Alone, that would be a pretty bad change for Sona because it majorly lowers her ability to use her abilities in different ways. If we make her goal into "always cast all 3 of my abilities in the same order to get the best power cord", then that takes away from the already relatively small amount of strategy that goes into when to use her spells.
Maybe it could work if she was redesigned and rebalanced to suit it, but if we were going that far we could find a better way. I can't get away from thinking that there would be much better ways to nerf her that don't feel nearly as bad for the Sona player and doesn't strip away her decisions.
Annie though... no chance. That change would be terrible for her.
Her entire unique value in the mid/late game, literally 100% of it, is reliable initiation. It's the only thing she has that other champions can't perfectly replicate. Because this is her one and only unique type of power, we can't just degrade it without making her always an inferior choice when compared to the unique strengths some other champion brings.
Make her stacks expire, and you either prevent her from initiating, taking away the only unique advantage she has over other champions and making it into something she does worse than them, or if the stack duration is long enough you force her to spam E to keep the stacks up, degrading the use case for that spell into "jam off cooldown no matter what".
Annie needs a more comprehensive rework. There is no "one change" that will leave her a useful champion while also fixing what people find obnoxious about her. If we take away reliable initation, then she needs an entirely new mechanic to be worth picking. As I see it that means that she either gets a full rework, or we leave her as is. Nothing in-between will suffice.