I just heard back from Anker and they had a bit more info. It looks like they couldn’t make it work reliably, and that’s why it’s not officially supported:
I confirmed with my colleague, the chips of the Liberty Air is different from the Liberty Lite model, and we do a lot of tests when we produce the liberty Air, and found if we want the liberty air support to use both sides separately, it will not work very well, in this situation, we cancel this feature, thanks for your understanding.
I also have already forwarded the website you sent to my colleague and let them check why this happens. Please note, if this feature can be used on some devices, the left side can only be used to listen to music, and you cannot use the left side to make a call.
It still doesn’t explain why certain devices are capable of using just the left why other devices are not. My current best guess is that some devices can understand the way the left earbud connects to the right, and they are essentially tricking the left bud into thinking that it is connected to the right. I don’t know enough about bluetooth to even speculate the technical reasons for my theory.