There are also ways to do Active Noise Cancelling without an external battery and without a new cable. I had an old Sony laptop that did ANR with software on the laptop and mics on the earpieces wired back into the laptop. Also the connector was backward compatible with a standard 3.5mm. They just used a 3.5mm connector with extra conductors on it like this one:
https://www.amazon.com/Connectronics-TRRS-Conductor-Metal-Au...
I had one of those tiny Sony Vaio's that did the same - great idea and tech but did you ever use it in comparison to the state of the art from Bose etc? It was night and day - the Sony was barely better than normal ear buds on an aeroplane...
I agree, I remember it being very poor compared to my Bose aviation headset. Still was a cool proof of concept. I imagine with the right software/hardware it could work just as well as external ANR