In mortgages, student loans, and healthcare, the government is already heavily involved on all aspects of the transaction. They might be providing insurance for a mortgage via FHA, student loan guarantees for a federal loan, or paying via Medicare. Private servicers/insurance are, in these cases, usually an unnecessary middleman that exists mainly to make a profit. In much of the rest of the developed world, the government acts as a single-payer for education and healthcare, and is more involved in housing than in the US.

Having the government take over supermarkets would be less efficient - it'd be adding complexity to the system, not reducing it.