Question: Where would you want to have the ability to be stable in all directions when moving and essentially not be throw-able? What circumstances could exist where this ability could be useful?
Let's think of it from that perspective..
Assuming I'm understanding the questions properly:
Always. Every circumstance. Part of my focus in ukemi is in how to find stability while in slightly-to-completely overextended positions. As Nage I'm trying to never be over extended (i.e. always stable in all directions). In both cases I'm trying to be nage, even if I might not be trying 100% such as in the case with brand new people, for example.