This gets to the crux of the problem, he had no idea if the ball was in play and didnt bother checking, he just assumed it wasnt. Despite never checking and making that assumption you have acknowledged he would still take the single had it been offered despite believing the ball was dead. You cant have it both ways. Taking the single despite having no idea if the ball is in play is fine but getting out isnt? sorry it simply doesnt wash with me.
The highlighted part is exactly why the ball is considered in play until both teams have deemed it is not and is exactly why Bairstow should have known better than to leave his crease until the ball was passed from keeper to another player or umpire had called over
I have never called to run a bye as the batsman at the strikers end. You are always called through by your partner who can see what is happening.
You are missing the point here. If there was a run Stokes would have called it. There was no misfield, so Stokes didn't react, so it's natural to think it's the over.
Everything that normally happens for the end of an over had happenned tbh. The ball was with the wicket keeper, he had fielded it cleanly, no run was being attempted, the ball was therefore at the right end for the next delivery.
The fact that they might have ran a bye in a hypothetical situation where the wicket keeper failed to field the ball, isn't really an issue as far as I can see. The ball isn't dead if someone misfields - I wish it was with some of the mistakes I've made in the field lol