The main problem they have with him is that back in around 04ish Shibata was positioned alongside Nakamura and Tanahashi as the three main superstars for the future. Along the same lines as Hashimoto, Chono, Muto were pushed as the main three in the 90's. But the company wasn't drawing much at all at this stage and Shibata decided to bounce and do freelance wrestling and, mostly, MMA. After his MMA run had pretty much ended he came back to wrestling. Tanahashi had become a pretty good draw at this stage, probably the best in Japan, and, as we've seen, NJPW has been on a bit of an upswing over the past few years. Shibata was rehired by NJPW but Tanahashi holds a grudge against him for leaving when the company was at a low point. It's unlikely he'll ever be given a huge push because of his past, it's probably mostly just to keep on punishing him but maybe a little because they feel they can't trust him fully even now.
I think that's pretty much it, others may have more info and more to add.