The Beaglebone is based on an SOC from TI that was designed for (at the time High End) Smartphones. Therefore it supports much lower power consumption and idle modes.
The BCM2763 and BCM2835 are the same silicon in a different package: https://raspberrypi.stackexchange.com/questions/840/why-is-t...
The trick/indicator about the design goal of primary Smartphone SOC usage for the OMAP SOCs and most mobile CPU is the existence of deep sleep, RAM retention modes. Additionally every GPIO pin is configurable for Pull-Up/Pull-Down to prevent current leakage.
I haven't looked extensively but I don't believe the Broadcom SOCs support this mode.
Actually after more extensive review - I think the story is probably that Broadcom attempted to make a smartphone processor from Alpamosaic's Video Coprocessor, but didn't adequately support the low power modes and didn't get any design wins for smart phone.
They then pivoted and found traction in the Over the Top TV space.
https://www.computer.org/publications/tech-news/chasing-pixe...
[0] https://www.anandtech.com/show/10716/roku-unveils-streaming-...
Roku Ultra: 900 MHz Broadcom BCM2836 CPU (quad-core)
[1] https://www.anandtech.com/show/4903/roku-2-xs-review-streami...
[2] https://www.reddit.com/r/raspberry_pi/comments/egwo6z/was_th...
But honestly, if you're going to that length and really need good battery life, maybe consider a fast microcontroller ;)
Another idea is to use an open source "smartphone" like the PinePhone as a battery-powered, pocket-sized, general purpose computer, like the RPi. (Depite whatever usage the Pine64 folks and "app" contributors envisage.)
The PinePhone boots from SD card, like the RPi. It will run Linux. What remains is further OS support. It will boot NetBSD, which is a start. The RPi battery problem has been solved.
For the avoidance of doubt, "general purpose" means, among other things, "cellular calling" is not a prerequisite to usefuless. Similarly, "pocket-sized" does not imply that the computer is always operated by removing it from a pocket and holding it in the hand; it refers to the form factor, not the usage.
Further, I am not seeking to stimulate discussion of "average users". This is "Hacker News" not "Average User News". The idea has come up a few times on https://forum.osdev.org but I have not seen it discussed on HN.
ARM11 is what the raspberry pi 4 BCM module uses from what I could tell. Looks like your best bet is to set the cpu freq down. I didn't see anything useful in the Broadcom BCM2711 datasheet.