Ppl seem to forget how manipulative Edward was. The Windsor genes include woe-is-me whininess and manipulation.
Edward hated being abroad and he used his brother's death as a means to come home. If he came home, the press would have known about it and sniffed around. George did not need the press backlash of why the heir cannot do his job.
This letter was Edward acting out because he did not get what he wanted, so he tried to manipulate the situation. This letter has been hinted at for a while by historians. The government kept copies of all of Edward's letters to anyone that was not BRF. This is just the first time the original was released.
So what does he do? He writes to his mistress, knowing fully well that every letter he wrote would be opened and it's contents retold to his father, and says all of these horrible things about his brother and how his family feels about John?
Edward was a whiner who was lashing out and knew that the things he wrote to his mistress would end up revealing themselves to his father. From what I know about George and Mary's relationship, George wouldn't tell Mary about certain things to avoid upsetting her and instead he would just get really angry. That's why nobody in the family understood why when Edward came back from his posting, George refused to even look at him. Would not look him in the eye, completely ignored him as if Edward did not exist. This was un-categorically George.
Mary was trying to soothe things over between them for MONTHS. She was sad that John just died and did not want another son gone. Normally George blew up and yelled at Edward, so to have George not even acknowledge Edward's existence was a huge strain in the family at the time. Mary actually thought it was because George found out about another mistress that was talking and tried to talk to Edward about settling down. Poor Mary thought it was just about Edward not being a proper gentleman. From what I know, it was not until after the abdication that Mary found out about the letters. I remember I read a passage where someone quoted her as saying "Poor poor George. Poor poor George", which really confused people. That reaction made the papers and everyone thought it was because Edward disappointed George, yet again. This caused another flurry of letters from Edward (who could never forgo the temptation to make himself look like a victim) saying how cruel Mary was for thinking about George and not him.
Yes, George and Mary did not want the public to know about John--but that was also advised by parliament. But to say that nobody loved John or that he was an animal was excessively cruel. John's death did take a toll on King George. He was very depressed for a while in private. Many were concerned about his mental health as a result. He took the death of John harder than Mary.