Where I live, the great majority of therapists and psychiatrists do not take insurance - specially the well-established ones that can get a lot of clients who pay completely out of pocket (essentially, a lot of providers cherry-pick their clients).

The reason they do this is that dealing with insurance panels is a pain. They have to get on the panel, often fight for reimbursement, have their sessions limited, and make a lot less money than when they get paid cash.