Should Canada severe their ties to the British Monarchy?

Prince Charles is currently in Toronto...But does anyone care if the heir to the british throne which supposedly has a lot to do with our Government, is here ? It doesn't appear so, because whatever he's coming for (I think it's the winter agricultural fair ), to make an opening speech, we're having trouble selling seats for. This had me wondering about how much do British Royalty have to do with canadians, and would it really make that much of a difference if we didn't have them anymore?