Non-bayesian estimation should use quasi-Maximum likelihood standard errors
At present, with non-Bayesian estimation, Dynare computes standard errors using the Hessian of the likelihood. This is only valid if it is assumed that the shocks in the "true" model are normally distributed. And, in that case, it is an inefficient way of computing the standard errors, as it will be equal to the Fisher information matrix, which only requires the calculation of the derivative of the score vector.
It would make more sense to default to computing quasi-Maximum likelihood "sandwich" covariances, with the option to use the Fisher information matrix if the user wants quicker results.