\(r_D\) is the required return to debtholders. Once we have taxes, the cost is lower \((1-t)r_D\)
Consequently, the cost of financing overall gets lower (WACC)
Since we only have corporate tax, the amount equityholders require is the amount I must pay, so there is no benefit in this case of taxes.
Your intuition is kind of correct, though. We could correct everything and obtain the after-tax equity cost:
\(r_E = r_{WACC} + \dfrac{D}{E}(r_{WACC}-r_D(1-t) )\)
You should obtain exactly the same value as with the method in the Excel sheet