is there a real, sensible reason why Annie throwing Tibbers is a bad idea from a gameplay perspective?
From a gameplay standpoint, short-ranged reliable instant initiation is pretty much the only unique thing Annie has going for her. It's something she does that other champions (particularly in her class) don't do, and it's pretty much the only valuable thing she really has that other champions don't. High reliability is unique, and it is Annie's niche. Increasing the range on her ult while giving it a delay isn't unique (much less particularly valuable or interesting). It's not giving her a reason to be played over other champions. It wouldn't leave her as either a balanced or an interesting champion. It would just feel bad.
Hell, Annie's still fully capable of Flash W for an instant AoE stun if she's allowed close enough.
That seems like a very good argument for not changing it. If she can still do almost the same thing in a less interesting way, what's the point of the change (unless we're appealing to people specifically annoyed by Tibbers but not by reliable initiation)? If reducing the range of the initiation was the goal, we could slightly reduce the range of tibbers and accomplish the same goal without removing iconic moments.
This idea has been repeatedly suggested by the community
That is a perfect reason to be cautious about the idea. The community's suggestions about how to "fix" champions they dislike tend to be less interested in making the champion unique and fun, and more interested in making sure they aren't bothered by it.
Personally, I think the community's suggestions for Annie are always terrible, and Riot is very smart to not agree with them. Most of them don't even try to give her a new identity or acknowledge how important reliability is to her right now, and would gladly leave her without any unique aspects just to get rid of the one thing that annoys them. I don't even like the state Annie is in right now, but it's still better than her having nothing unique to her name at all.