The main problem I'd have with Bairstow coming back in again, is that he hasn't had a chance to fix his problem.
I doubt that he would ever be the Bairstow that once looked legitimately good in tests.
On the other hand, forcing him into test cricket could impact his game in ODIs too. He has a claim of being possibly the greatest ODI opener ever in history (averages close to 50 with a strike rate of nearly 105). Why would you want to potentially ruin that when you have better alternatives now in tests?