Some real misunderstandings of the issues here.
Firstly with Bairstow, the only thing that will have happened is that McCullum will have reassured him that he is a guaranteed pick. The issue isn't liberating him or anything like it - it is simply that he has been horrendously messed about by the Test management over the last six years - keeper, 5 bat, keeper, three bat, out of the side, six bat etc etc. And at every stage having it made clear that despite all of the evidence that he is both a better test batsman and better test keeper than Goldenballs, Goldenballs will get first pick of the opportunities at every stage. He has made four tons in his last seven tests, played two of the best knocks any of us have seen back to back, and there are still a lot of people on here who would drop him if he got bowled through the gate against India next week.
Will Buttler come back? I wouldn't rule it out, but I don't think it is the certainty some people do. He will have the captaincy of the white ball sides by the end of the Summer and that is probably enough.
Now Foakes. Yes, statistically he has dropped a lot of chances. But the fact is, most keepers would not have got a glove to many of them - he isn't missing straightforward chances like, say, Buttler did, he is getting a hand on massive legside stretches and the like. Yes, the one he took out of Root's hands on the second morning was a misjudgement, but again he did everything right - his foot movement was exemplary, he had the confidence to go for the chance, the ball just moved away from him slightly.