It is true that Monte Carlo simulation (MCS) is often computationally infeasible in numerical structural reliability analysis. Especially if the analysis is based on computationally demanding models (e.g., finite element models), the computational burden to evaluate thousands of model runs is typically just too large. However, whenever it is computationally feasible to apply MCS, MCS is the most robust reliability method amongst all sampling-based reliability methods.
MCS is so robust because its performance does not depend on the particular formulation of the limit state function underlying the problem. It is the only structural reliability method whose performance depends solely on (1) the number $K$ of samples used to conduct the analysis and (2) the underlying probability of failure $p_f$. For fixed $K$ and $p_f$, the statistical performance of MCS will always be the same — no matter how the limit-state function is expressed and irrespective of whether the stochastic model is comprised of just a single random variable or millions of random variables.