I've started applying this and it's amazing how well this works.
Of course sometimes it's just not possible to reduce the scope any further, but the key point is that the stakeholders just want something, anything and as soon as possible at that.
You give them that and suddenly there's much less pressure and you can focus on delivering the rest, or sometimes dropping it entirely because in hindsight it wasn't that important.
There's a similar phenomenon occuring when playing planning poker - often the estimate is not what anyone wanted, but the one that the most could agree on, which is usually way off. I thought of solving this by having a single transferable vote, but I hadn't had a chance to play planning poker for over a year now, so I have no data on its effectiveness.