Most likely, Alexander III saw that all that formal training hadn't done his father Alexander II any good (it didn't save his life) and so thought that it was not something he needed and was not going to get for his own son, Nicholas II.
While Marie Dagmar was a perfect choice for Empress and she did her job with skill, she produced children who not physically anywhere near as impressive as did her in laws. She also spoiled Nicky and, I believe, coddled him. Perhaps to protect him from his massive father.
Somehow, IMHO, Alexander III thought that becoming Tsar was something that was absorbed by osmosis. After all, he had not had any special training and he believed he was doing just fine. And autocracy did seem to work under Alexander III. He was so repressive and reactionary that he forced the system to work, even if he had to do it from behind closed palace doors.
Autocracy was, after all, divinely bestowed. Whomever was chosen for the task by birth would just automatically know how to do the job when the time came.
Like almost all families, the Romanovs were quite dysfunctional from the time that Peter II had his son Alexei tortured and killed, though the murders of Peter III and Paul I and then the refusal of Constantine to take the throne because he liked being Governor of Poland and didn't want to give up that freedom.