What I don't get about your strategy:

Why not work on something so valuable that even if it takes twice as long as the best estimate, with twice the headcount working on it, it would still be worth it?

As a a manager, I feel that helping to find projects that have that amount of value is an important part of my job, so that if I am fighting for a project my team's working on, I'm actually in the right from a business case point of view, not simply playing some BS political game.

If there are no projects that fit that value filter, then that's a completely different organizational problem.