That example file is just that: A terribly obvious explanation of the issue to expose it. I'm not printing stuff that exposes the bug as directly as that, and you're right, without additional support on the sides it would probably tip before connected. And in that case I'd be happy to go in and manually place some support pillars to hold it up.
What I'm printing is akin to a cave roof with stalactites : S3d Won't catch any of the stalactite tips, so you have to manually place support for them all: If you miss any, you get spaghetti pouring from the roof of your cave. And sometimes this is non-trivial based on how the model was created, with external bits occluding the interior, and the already-existing support blocking your view as well (see below).
I encounter this issue infrequently, but that's where the problem lies: It's infrequent enough that I forget it's a problem. I expect the slicer to place supports where it should: If something is suspended in the air, and you tell your slicer to provide auto-supports, it's ironic it supports everything but the feature that need it most.
Here's another example:
Best model evar! Time to print!
Auto-added supports. Super supported no doubt:
Wait, why is part of it completely unsupported?
So trying to find all these unsupported areas while surrounded by valid support becomes a real pain on an asset more complex that this.