This is already done, as far as is possible.

When you are stationary Arc goes into a “sleep mode”, requesting only extremely low accuracy location data (eg location to nearest 10 kilometres). This allows the phone to power down GPS/GNSS services and provide location only by cell tower triangulation. It also reduces location update delivery to very low frequency.

During “sleep mode” Arc will periodically wake up (every 6 to 60 seconds) and request a high accuracy location update, to check to see whether you’re still at the same place. These wake up checks consume extremely low energy, and do not impact battery life.

Basically when you are stationary Arc is using as little energy as possible, while still retaining enough awareness to be able to restart recording as quickly and accurately as possible, should you start moving again. The energy consumption of this process can’t be optimised significantly beyond where it is now. (I’ve spent the last seven years of my life on it, so I say that with great confidence 😉)

If your phone isn’t lasting through the day, it won’t be due to Arc recording in the background. It will be almost entirely due to the apps you use in the foreground, which is where 90% of battery/energy use goes.

Any time you have the phone unlocked, screen on, energy use will spike to orders of magnitude higher than when the phone is locked, regardless of whether Arc is recording or not. The longer you have the screen on, apps in the foreground, etc, the faster the battery will drain. The screen and the CPU/GPU are the largest battery/energy consumers by far. While background recording consumes barely anything at all.

If you want more battery life each day, the easiest fix is to reduce your screen brightness. Beyond that, reduce time spent with the phone unlocked and apps in the foreground. All those UI updates that apps are doing are consuming orders of magnitude more energy than anything that happens in the background while the phone is locked and screen off.