Before revision:  This latter condition is often met in differences-in-differences designs, where the CATEs are estimators of the effect of having been treated for a certain number of time periods. In that case, the optimal estimator is no longer feasible , as it depends on unknown quantities, but a feasible estimator can easily be constructed by replacing those unknown quantities by estimators .
After revision:  This latter condition is often met in differences-in-differences designs, if errors are homoscedastic and uncorrelated. Under those assumptions, I show that the minimax estimator is still feasible and can easily be constructed by replacing those unknown quantities by estimators .