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And if neither of those things matters, why don't riders run deep rims all the time

Stability in windy conditions is the main reason not to use them

Riders will want shallow rims in the climbs because they make lighter, quicker accelerating wheels, good for attacking and keeping on an attacker's wheel.

This effect is deliberately blown out of all proportion by manufacturers of light, but not aero, wheels. You need to be going quite slowly for the 300g weight difference between Lightweights aand Zipp 404s to overcome the drag problem of the lighter wheel, and Lightweights are actually pretty aero for light wheels, some other weight weenie wheels are truly appalling when ridden outside a vacuum.