I've had the same experience with non-HMO coverage in the US.
With HMO's, you're guaranteed someone will be assigned to you. With traditional insurance, there's a big labor shortage, and there are often <= 1 doctors accepting patients in some towns.
You can't even shop around for a family doctor. You have to sell them accepting you as a patient. With that power inbalance you better follow what they suggest and avoid questioning too much or you won't have a doctor.