If 90% of people have the same basic insurance, medical billing becomes much easier. You no longer have to pay as many medical billing people to deal with 20 different systems. Reimbursements become known and clear-cut — it’s not a lottery, and you’re more likely to get paid a good portion of your bill. The collections people go away for the most part too. A lot of bureaucracy that’s responsible for qualifying people for different insurance programs goes away too.
I’m not advocating for true single-payer, just something like Medicare + Medigap. Private insurance will still exist, but it will play a secondary role.