About the health card and insurance, I suppose it depends on whether you're purchasing secondary insurance (the policy picks up any costs that are not covered by your primary insurance... you have to first claim through your health card, then, months later, after they decide how much they'll reimburse you, you can claim for the rest of your expenses through the travel policy). Primary insurance policies, where you don't have to claim through your provincial health card first, are more expensive.
I would take that advice about bringing your health card as a warning... you are buying secondary insurance, which means you will have to pay your expenses up front, then claim for reimbursement through your provincial health plan, and only then get to claim through the insurance you purchased specifically to pay for any emergency medical expenses.
But about leaving the ID at home.... with my luck, the place would burn down or get burgled! Or I might unexpectedly need to rent a car and need my driver's license. And credit cards... I know people who have had their accounts frozen or unexpected holds put on a card while traveling... luckily they had more than one card. I suppose I could do without my library card, my Starbucks frequent-buyer card, and I never carry my SIN card anyway. I guess the only solution is to make sure you have copies of vital ID packed in a separate place.