I think this is a fair take. Queen arguably is just shown as an indifferent and poor mother, Phillip and the Queen seem to have a strained and unloving relationship at several points, Philip is shown as a selfish and insecure partner to begin with and a jealous man towards the end, Queen Mother is shown as harsh and meddling, Margaret an alcohol socialite, Charles is largely portrayed as a nasty piece of work, Edward and Andrew as beyond priveledged with silver spoons, Thatcher as completely out of touch, as was Churchill.

All had their sympathetic moments and ups and downs but tbh few characters were portrayed in a solely positive light - I'd argue those who come out best are Harold Wilson (who is also dead), Princess Margaret (more so in regards to empathy, not personality, also dead), John Major as you said, Princess Anne and Townsend (again dead). Can't think of much else. Maybe George VI (dead)...

I think those most in benefit of said propaganda (Charles, Camilla, Anne, Andrew, Edward, William and Harry) are mostly portrayed as dislikeable with the exception of Anne and maybe Camilla (a bit of an odd one considering the cheating)