The UK has similar. Single payer rather than public insurance, but people can buy private insurance if they want. It's certainly a small minority who do: it's largely a perk for some senior jobs, along with the BMW. It's relatively cheap (around £50/month for a non-smoker in their 30s), because all of the basic stuff is already covered by the NHS. The private insurance is mostly about getting shorter waiting times for elective surgery, and maybe a nice room.