We study the $L^1$-approximation of the log-Heston SDE at the terminal time point by arbitrary methods that use an equidistant discretization of the driving Brownian motion. We show that such methods can achieve at most order $ \min \{ ν, \tfrac{1}{2} \}$, where $ν$ is the Feller index of the underlying CIR process. As a consequence Euler-type schemes are optimal for $ν\geq 1$, since they have convergence order $\tfrac{1}{2}-ε$ for $ε>0$ arbitrarily small in this regime.