At least on mobile SoCs that's exactly how it works, in fact due to how dynamic frequency scaling works it can be worse than 2x because to run at a higher frequ

At least on mobile SoCs that's exactly how it works, in fact due to how dynamic frequency scaling works it can be worse than 2x because to run at a higher frequency you need to run at a higher voltage. Your frequency increases(which drive switching costs) and you're paying more per current due P=IV. You're right in that not running the workload if possible is the best power savings but if you can't do that moving it to more efficient usage is a good way to make large inroads on power usage.