No one expects him to be Neymar. At all.
Allegri is allways very careful introducing new players, but its not stubborness, and defenitely in Costa's case he hasnt done enough to dissaprove Allegri (unlike Morata who were better then Llorente after a while).
We are in it to win it, so as great giving continuity is, you cant do that for someone who doesnt earn it in the minutes he gets. Cuadrado plays better then him, difference is close, but as overall team player, passer, general decision making, Cuadrado is ahead and Costa needs to find way to have balance in his game and play less brainless as he has been doing. Find his niche and make more of an impact. Its all on him. No one else.