I'm going to go against conventional wisdom. Sorry. Higher cadences do not reduce the amount of work you do. They increase it. The reason for higher cadence is to reduce risk of injury to your knees. So the trick is to find a cadence that is not too fast that it wastes energy but not so slow that you hurt your knees. My feeling is that for tough climbing, it's way, way below 90 rpm.

I also feel that high cadence climbing does little to build ability to climb. I think it hinders it, because climbing is an opportunity to push harder on the pedals than any other time. I couldn't climb well until I got a fixed gear (66 inches) and didn't have the opportunity to shift down. You don't need a fixed gear to build this skill. You need to choose your gear well.

Plus standing up helps you put more force on the pedals.

I'm willing to talk more about this if you like. I've been cycling seriously for 34 years, and this is what I've learned.

High cadences are fine for flats and downhills but I think they are bad for vigorous climbs.