I suspect most of us were brought up not to 'show off' , show strong feelings or see ourselves as the centre of the universe. The stars of old were less reserved, no doubt because of the drama that accompanies so much theatrical or film life. I don't feel we are unpleasantly touchy feely as some posters seem to.
I see it as a positive thing that our society is less inclined to expect feelings to be suppressed. How many of us knew fathers (in my case, not mine luckily) who had suffered eg on the Burma railway. I know men who never talked about, or sought help but who drank, had outbursts of anger and endless nightmares.
So far as the death of Diana goes, I wore a Don't do it Di badge when her marriage was being planned. She was 19 years old, had experienced a difficult childhood and marrying the future king within days of discovering he was romantically involved with Camilla. She struggled with her new life, didn't have the coping mechanisms needed. I'm sure both she and a Charles were miserable. Her death was a tragedy. The royal family seemed to attempt to protect William and Harry by staying away from London but I don't accept most people could believe taking two boys to Church, in public, within a couple of hours of telling them their mother was dead, was in any way protective. The family were in shock,like most people. There was some public anger expressed but that dissipated as soon as they returned to London. The Queen is extremely popular. I wasn't a Royalist as a younger woman but she acts well as out head of state.
I don't see that 'the same is happening now' as the op suggests. I do feel Theresa May is having a torrid time but I don't think that's what was meant. I may of course be wrong.
So, I don't believe our society is to Americanised. I don't know enough about celebs to criticise. I've only seen Lily Alen being interviewed and I couldn't find fault with her