You make some good points but there are some significant distinctions ...
The public response to Kennedy's death had a lot to do with its' horrific manner and that Americans were determined to show that they would not be cowed or beaten by such acts ... a far better comparison would to compare the public response to a President dying of old age. The Queen's death was sad, but not tragic or horrifc - she had a good innings and died of old age - the turn out is one of sadness, affection, admiration and respect - it is not undepinned by defiant, outraged nationalism combining with the grief - like JFK's.
As for Ghandhi, India is a deeply religious country and it can't be denied that much of the grief and mourning stemmed from that perspective. It was hugely domestic.
We are a largely a secular nation so we can't really ascribe religion as a major factor for the numbers turning up - despite her being head of the Chiurch of Endland - nor does it play a part in the thousands of foreign visitors feeling a need to pay their respects.
As to whether the monarchy is archaic and wrong? I think that is a matter of opinion and for debate. The monarchy in this country has been largely symbolic since right back to Elizabeth I - they don't really have much say in running the country - what really is archaic and wrong us That decisions that affect everyone's lives have been, and continue to be, made by a bunch of self-serving, amoral, public school twats - irrespective of the political party they are affiliated to