I mean, your experience in the US is exactly like mine in European public care system looking for a psychiatrist or other more niche doctor: Multi month long waiting lists, doctors who are full and don't take any new patients, needing to go private out of pocket. Even the good private ones are booked weeks into the future.
But it is the private health care in US. There is no other option unlike you who can choose to go private. And I would guess that your out of pocket payment will not cause you to go to bankruptcy.
