But can A10 handle the coordination involved between a phone and an AppleTV so that it can show the image on one but use the camera and microphone on the other but keep them in sync?

I looked up the specs, and the biggest glaring omission is that the A10 (not A10 fusion), does not appear to have hardware encoding of HEVC.

The Apple TV has to stream camera from the iPhone to the TV and the other participants (up to 32 participants) in real time without dropping frames or garbling the audio.

I'm not sure the the A10, say nothing of the A4, could reliably handle group calls. To be fair to the A4 and A10, group calls weren't a feature of FaceTime until 2018. Could the A4 handle an audio or low-res video call? Probably.

> Facetime came out in 2010 on the iPhone 4

You have a great recall of the timeline. I thought that it came out much earlier but I was mistakenly thinking of iChat AV. "In June 2003, Apple announced iChat AV . . ." [1]

0. https://en.wikipedia.org/wiki/FaceTime

1. https://en.wikipedia.org/wiki/IChat

FaceTime in full HD was not supported until 2020, and it was only on devices that released in 2017 or newer. It is more than just a 'call'

Whatever hardware they use for near field comms between the phone and the TV maybe?