  The efficiency at the maximum power (EMP) for finite-time Carnot engines
established with the low-dissipation model, relies significantly on the
assumption of the inverse proportion scaling of the irreversible entropy
generation $\Delta S^{(\mathrm{ir})}$ on the operation time $\tau$, i.e.,
$\Delta S^{(\mathrm{ir})}\propto1/\tau$. The optimal operation time of the
finite-time isothermal process for EMP has to be within the valid regime of the
inverse proportion scaling. Yet, such consistency was not tested due to the
unknown coefficient of the $1/\tau$-scaling. In this paper, using a two-level
atomic heat engine as an illustration, we reveal that the optimization of the
finite-time Carnot engines with the low-dissipation model is self-consistent
only in the regime of $\eta_{\mathrm{C}}\ll1$, where $\eta_{\mathrm{C}}$ is the
Carnot efficiency. In the large-$\eta_{\mathrm{C}}$ regime, the operation time
for EMP obtained with the low-dissipation model is not within the valid regime
of the $1/\tau$-scaling, and the exact EMP is found to surpass the well-known
bound $\eta_{+}=\eta_{\mathrm{C}}/(2-\eta_{\mathrm{C}})$
