I climb at a lower cadence than on the flats, usuallly 70-80 vs 90+, with gears to spare, so it's not a matter of running out of gears per se. My typical climbs are around 6%-9% and I have gearing suited to that. For steeper sections I don't mind grinding it out. I'm not going to carry gearing that I won't want 99% of the time.
Unlike almost most of the answers to the OP's question this one doesn't make the poster look an idiot or a braggart.