There are many OECD countries where primary care appointments are not free. France, Switzerland, Japan, etc.

Countries that do make them free still have some sort of rationing mechanism that prevents primary care practitioners from being overwhelmed. In the UK, for example, appointment requests are triaged based on urgency and non-urgent appointments will often have to wait a while. In Canada, it's somewhat quicker to get appointments with your provider but much harder to find a provider if you don't already have one.

More generally, the goal of a functional healthcare system is to make sure everyone gets the care they need to achieve good health outcomes, not to ensure that everyone can have as much of a doctor's time as they'd like.