This GCN Video was posted about a month back where they did a test of climbing a 5.6% hill at 325 watts average using shallow rims and then deep section rims on the same bike (16:52 vs 16:55). They found that using shallow rim wheels on the bike was faster than using the aero rim wheels.
This goes to prove what all the pro cyclists already know when they switch to shallow rim wheels for races with big climbs. Shallow rim wheels do indeed climb faster than deep section rims. And the testing didn’t even include having to do accelerations uphill that is typical of bike races.
It is a myth on here that deep section wheels are always faster. The wheels have micro-accelerations when going up hill because there is always the dead spot in everyone’s pedal stroke where no power is applied. The wheels slow down due to gravity pulling down and then you have to micro accelerate it after the dead spot is over. Add that up over a big climb and the gains can be significant, especially if you have to chase down repeated attacks.
A wheel with lower rotational weight will have the advantage going up hill because there is less rotational weight you have to overcome with each pedal stroke. It also explains when people’s cadence and pedal stroke mechanics going up hill is different than on flat ground. On flat ground it takes much longer to slow down if you stop pedaling so the dead spots in everyone’s pedal strokes simply don’t matter very much.