Service? Name one thing she accomplished besides “existing.”
I guess it depends on how you define 'accomplished'.
Granted, she has never ended world hunger, or cured the world of some horrible disease. But, she did provide a certain function to the UK (and to the lesser extent Canadian) government that may not have been earth shattering or spectacular, but had some usefulness nonetheless.
There is a certain value in having a non-political head-of-state, even if it is just for ceremonial purposes. For example, when she grants knighthoods (or when the Canadian gov general grants the order of Canada), it is not "the conservative/labor/liberal/etc. prime minister granting the award", but someone who is not tainted by "which party do you belong to". (And if you don't see the value in that, just look south of the border, when President Stubby McBonespurs attended a ceremony to honor Native American WW2 vets, and proceeded to make various racial slurs and political insults.)
And while her reign wasn't 100% perfect, it was much "cleaner" (i.e. fewer scandals) than any political leader would have had in the same time period. You would hope that a king or queen would act dignified (while at the same time living life under constant scrutiny) and she managed to do that.
And lets look at a few of the other things she has done:
- She (as well as many other royals) served in the military. (In the case of Queen Liz she was a mechanic and driver, I think involving ambulance services)
- As previous royals had done (and as King Chuckles is doing) she has turned over most revenue from various royal properties (which are technically the property of the royal family) to the government (in exchange for a yearly stipend). This is a voluntary practice, but the net result is that the government benefits from millions of dollars per year. If she wanted to be greedy, she could have just said "screw you, I'm keeping all the profits", but she didn't.
- It is estimated that her involvement in various charities has contributed to them raising over 1 billion pounds over the years.
See:
https://www.theguardian.com/voluntary-sector-network/2012/jun/11/queen-charitable-support