iOS 12 is indeed faster, but it seems to be at a cost to increased battery usage. From my understanding, CPU is ramped up to maximum performance mode when needed, like launching applications and other demanding tasks. Then dialed back down when not needed. It could be just the normal beta battery usage issues, but mine gets hit hard.

getting the work done as fast as possible then shutting down is usually the way to get the best battery life.

We're talking about a blur animation though. It's not a fixed unit of work. The way to get the best battery is to render a cheaper blur that still looks fine.

No,

Power consumption scales roughly quadratically in relation to frequency.

Modern cores all have features like power and frequency gating, performance counters - the stuff needed to allocate just enough of computing power to complete computations in time. This is very, very evident in things like music playback - a lot of intermittent io and computational spikes.

Well, yes. This is known as the "race to sleep" and is probably the single most common power saving strategy for modern chips.

It's true that switching power scales with the square of voltage (P=V^2Cf), but that's not really a problem for the race to sleep as switching power even with V as low as you can get it is going to be orders of magnitude higher than your static power.

No, no, no, there are a lot of situations where you can't sleep the chip.

The "race to sleep" is a misconception long held by software people.

The situation you describe is only true when the part of the chip doing computation is completely off, and is shunted off from power. That's so called deep sleep.

There is a limit to how frequent you can switch the big and complex chip to low power state, as doing so by itself takes some power and computational overhead to keep track of your power use profile.

For many cases, one have to endure leakage and keep working, like when you have to do IO have to keep the chip "on" anyways, and want to utilize your "on" time as much as possible.

A ton of work have been done on power saving strategies like partial device shutdown, shutting down part of registers, trying to operate different parts of the chip at different frequencies to match io wait and processing time, downshifting to more iterative computational paths, and on and on and on

I would agree, but doesn't seem to be the case here! This is also with a new(6 month) battery. It's either ramping up for much too long, or it's just normal beta battery usage.

Isn't that exactly what it should be doing? Was it artificially capping CPU clock before just to save battery?

It's a beta... even .0 releases have poor battery life. Give it some time.