As you probably already know, it really depends on your climbing style. I'm heavy. I climb at a relatively slow cadence with lots of torque, so I move back on my saddle to engage my gluts. Lots of climbers do this, which is really my point in arguing for keeping the back half of the saddle.

As far as power goes, it's actually a function of your hip angle. The more closed your hips, the more you engage your big glut muscles and the more power you have. You are on the tip of your saddle in a TT because you are bent way far over for aerodynamics and have to open your hips just enough to let your thighs clear your chest (also, if you are a guy, stuff is just... in the way). There is also the leverage aspect. The weaker your core, the more you sit on the nose of the saddle during hard efforts because you need the extra leverage to counter the force from your legs.