The King or Queen of England is also the King or Queen of Canada. He or she is our head of state. In Canada we have a Governor General who is appointed by the King or Queen on the advice of Canada's Parliament to act in the King or Queen's place as our Head of State in his or her absence. The King or Queen and Governor General's positions are purely ceremonial positions (they have virtually no power) though the Queen is said to have asked and required answers to tough and exceedingly uncomfortable questions from time to time at her weekly meeting with the British Prime Minister (the elected Head of Government in Britain).
The King or Queen or Governor General has one important power. They appoint the government following an election and can deny a request to form a government or call an election. Recently in British Columbia the former Premier won fewer seats at an election than the other two parties who stated that they were willing to form a coalition government. The Lieutenant Governor (the equivalent of the Governor general at the provincial level) refused to let the former premier form a new government and accepted the offer of a coalition. The former premier (who had won the most seats but had no majority) in theory could have formed a government, been immediately defeated in a confidence vote, and demanded a new election. But the Lieutenant Governor wouldn't let her.
Queen Elizabeth was generally quite popular in Canada as is her grandson William who will become King on the passing of King Charles.
Does it work? Yes, quite well actually.
Could it change? Sure, but all 10 provinces and the Federal Government would have to agree on a mechanism to appoint a new Head of State. But they will never all agree so no it can't be changed.
Naturally, as the Head of State, King Charles now appears on our currency.