Pre-silicon side-channel leakage assessment is a useful tool to identify hardware vulnerabilities at design time, but it requires many high-resolution power traces and increases the power simulation cost of the design. By downsampling and averaging these high-resolution traces, we show that the power simulation cost can be considerably reduced without significant loss of side-channel leakage assessment quality. We introduce a theoretical basis for our claims. Our results demonstrate up to 6.5-fold power-simulation speed improvement on a gate-level side-channel leakage assessment of a RISC-V SoC. Furthermore, we clarify the conditions under which the averaged sampling technique can be successfully used.