a) I don't see reports from people with other phones. The post in the linked thread with the iPhone 7 is most probably another issue with using multiple different BT headsets at the same time.
"I don't see reports from people with other phones ... oh, you mean this one I'll cherry-pick? Well, uh, it must be a different issue because of this detail that doesn't apply to that other report with an iPhone 7 that I didn't cherry-pick." Sure, sure.
b) I assume your other BT headsets are single devices. The problem with the AirPods is that the phone needs to provide two separate streams which is a whole other game than single stream audio.
b1) not if you're only using one of them, which I have done and still see the issue, and
b2) "The problem with the AirPods is..." Ah, you know the root cause of the issue! That's wonderful! You should ring Apple and let them know what you've discovered. If that Apple Support Community thread is to be trusted, apparently Apple engineers are still in the data collection phase of investigating the issue. You're ahead of the game!
c) I just tested them with my iPad. I just picked up the phone using continuity (phone call to 6s -> picked up via iPad -> AirPods connected to iPad) And they work perfectly.
This is not particularly relevant, as this may very well be an entirely different scenario on the backend than having AirPods connected to an iPhone.
Actually, we already know it is different on the backend because we already know the AirPods don't automatically switch their connection to/from iPads and Macs like they do between an iPhone and an Apple Watch (a feature that some have theorized may be related to the issue).
Now, just to be clear, I'm not saying the root cause of the issue isn't something to do with the phone... or even that it isn't something to do with 6s or 6s Plus phones specifically. All I'm saying is that we don't know what the root cause is yet, no matter how some of us may want to read the tea leaves of generally unreliable internet testimonials.