Low-numerical-aperture (NA) step-index ultra-large-mode-area fibers are of considerable interest for high-power fiber lasers because lowering NA enlarges the effective area of the fundamental mode and suppresses nonlinear effects. However, it also increases bending sensitivity and thus limits the applicability of bend-induced mode control. In this work, a systematic numerical investigation is carried out on step-index fibers with low NA values of 0.04,0.03, and 0.02. The bending losses of L P_01 and L P_11 modes for different core diameters are calculated by using the finiteelement method combined with the equivalent refractive-index model, and the variation of the effective area of the fundamental mode is analyzed. The results show that, corresponding to the wavelength of 1060 nm, for fibers with NA of 0.04 and 0.03, bend-induced mode control is feasible within appropriate core-diameter ranges. For core diameters no larger than 30 \mu \mathrm~m and 35 \mu \mathrm~m, respectively, L P_11 mode can be effectively suppressed with a bending loss of not less than 10 \mathrm~dB / \mathrmm, while the effective area can reach 561 \mu \mathrm~m^2 and 873 \mu \mathrm~m^2 respectively. When the core diameter is up to 50 \mu \mathrm~m, only L P_11 \mathrme mode can be suppressed by bending, and the corresponding effective area is approximately 778 \mu \mathrm~m^2 and 1176 \mu \mathrm~m^2 respectively. Further reducing NA to 0.02 enlarges the effective area, but the sharply increased bending losses make bend-induced mode control impractical. In this case, straight-fiber single-mode design is more suitable for exploiting the mode-area advantage brought by low NA. These results reveal the trade-off between mode-area scaling and bending sensitivity, and can provide theoretical guidance for the design of low-NA large-mode-area doped fibers.