As a SIMD noob, one thing that wasn't obvious to me is that SIMD can also speed you up if your mem throughput is underutilized by having the CPU load more data per instruction. It isn't just about compute speedups, which is typically what it's advertised for. Using perf on Linux has been very educational for me to get an intuition for modern CPU performance.
The way simd speeds up "compute" is indeed mainly the reason that you operate on multiple pieces of data at once.