Indeed, and there's a thing called "race to sleep". That is, you want to light up as much of the core as possible as fast as possible so you can get the CPU back to idle as soon as possible to save on battery power, because having the CPU active for more time (but not using as many circuits as it "could") draws a lot more power.

At the same time, it takes a certain amount of time for a CPU to switch power levels, and I remember it being surprisingly slow on some (older?) processors.

So in Linux (and I assume elsewhere) there were attempts to figure out if the cost in time/power to move up to a higher power state would be worth the faster processing, or if staying lower power but slower would end up using less power because it was a short task.

I think the last chips I remember seeing numbers for were some of the older Apple M-series chips, and they were lightning fast to switch power levels. That would certainly make it easier to figure out if it was worth going up to a higher power state, if I’m remembering correctly.