In the real universe - one game 7 win away from a return trip to the finals - I think Mazzulla has done well enough to merit a return, none of the key players have played their way off the team, etc.
I'm not sure that White not being there at the end or missing the layup or not having time changes much. Still basically the same situation. Maybe it changes the evaluation of White's role going forward. (As in, what he did do last night should elevate him in the eyes of the organization).
Mazzulla has upped his coaching game during this series, after the team fell behind 3-0.
At the same time, the team's halfcourt offense is stupid, and stagnant, and overly reliant on individual physical dominance by their star players, and Miami's less talented but more disciplined defense shows the flaws of that approach. (By contrast, the Celtics transition offense is smart, fluid, and creative - of course it also relies on the individual physical dominance of the players, but it also has good decision-making). And the Celtics halfcourt offense never looks worse than when they are deliberately trying to play slowly and run time off the clock to protect a lead - that style even seems to detract from the defensive focus.
Clearly some of the lessons of last year were not learned, and some type of changes need to be made to address that. But I think they have hit a point, even if they had lost last night, where more minor changes were in order rather than major ones.