Considering the paradigmatic example of driven Brownian motion, we perform extensive numerical analysis on the performance of optimal linear-response processes far from equilibrium. We restrict ourselves to the overdamped regime where exact optimal processes are known analytically and several experimental realizations have been implemented. This allows us to make a fair comparison with the optimal processes obtained in linear response and address their relevance to experiments. The investigations we present use parameters values taken from feasible experimental setups. Our results also help to delimit the range of validity of the perturbative descriptions of the irreversible work. Nevertheless, our main result is the fact that optimal linear-response processes can perform surprisingly well far from their expected regime of application.