The advantage of using heteroskedasticity-robust standard errors is that:

that they are easier to compute than the homoskedasticity-only standard errors

they produce asymptotically valid inferences even if you do not know the form of the conditional variance function.

it makes the OLS estimator BLUE, even in the presence of heteroskedasticity

they do not unnecessarily complicate matters, since in real-world applications, the functional form of the conditional variance can easily be found