The described issue arises from how structs work in C# (they are value type). Both ScriptableCullingParameters and CameraProperties are structs. CameraProperties is accessed through a public property on the ScriptableCullingParameters. To get the expected behavior you thus have to write the properties back;

void DemonstrateApproach()
{
Camera.main.TryGetCullingParameters(out ScriptableCullingParameters p);

Debug.Log($"before: {p.cameraProperties.GetCameraCullingPlane(0).normal}"); // prints before: (0.7, 0.0, 0.7)
var properties = p.cameraProperties;
properties.SetCameraCullingPlane(0, new Plane(Vector3.up, Vector3.zero));
p.cameraProperties = properties;
Debug.Log($"after: {p.cameraProperties.GetCameraCullingPlane(0).normal}"); // prints after: (0.0, 1.0, 0.0)
}

Many IDEs such as Resharper will highlight issues like this. In case you want to know more about the details consider reading this page; https://stackoverflow.com/questions/34906823/c-sharp-getters-setters-in-structs-and-interfaces