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.