Regarding whether Medicare for all is Socialism or not you first have to understand that there is not a precise, universal agreed definition of Socialism.
Merge is using one definition and based on that definition one can conclude that it is not socialism.
However, other definitions of socialism talk about other forms of production ownership and control. One definition that regulation of industry and services by the Government is Socialism.
For health care, IMO, if the government is controlling all payments to providers, that constitutes Socialism.
That aside, people should take a hard look at how this might actually work.
With Medicare today, you go the provider and get treatment. They send a bill to Medicare. Medicare pays perhaps 20-50% of the bill. The provider then sends the remainder to secondary insurance (a.k.a Medigap) if the patient has it. Secondary insurance is paid for by the patient. If the sum of the reimbursements is less than the fee, the provider chooses to either write the balance off or bill the patient for some or all of the balance.
I have client who is a CFO of Health Network. They lose money on the Medicare Patients and make it up with private pay and regular HMO insurance patients.
If you take away the current economics of private pay and HMO insurance, you will have a system that will not cover the cost of the providers.
Some of the shortfall will be covered by increased Medigap premiums.
Some of the shortfall will be covered by reduced care,and wait times.
Some of the shortfall will be covered by increase Medicare deductions (a.k.a payroll taxes)
Some of the shortfall will be covered by increased federal debt.
Some providers will fold and put pressure on provider supply, i.e more wait times.
At present, the competition among HMOs and their ability to negotiate with the providers is keeping this fragile system alive. When you take that away and turn over complete control to the government, the promise of "free healthcare" will manifest as a disaster.