The federal government should "step in" how, exactly?
Evrery year, they already tally up what provinces charged for private care, and deduct it from their next transfer payment. This is publicly reported. That's as much as the Canada Health Act allows them to do.
canada.ca
Canada Health Act Annual Report 2024-2025 - Canada.ca
Health Canada produces an Annual Report on the Canada Health Act each fiscal year with information on Canada's federal health care insurance legislation and how it defines the national principles that govern the Canadian health care insurance system.