This is a common misunderstanding about H-1B. For hiring someone on H-1B, the employer need not prove that they made attempts to hire a citizen or permanent resident first. But to sponsor an employee on H-1B for green card, they have to provide such a proof. What you describe happens during that process - you have an employee you are happy with, want to sponsor her for permanent residency in the country, and are willing to go through the expenses, but state insists that you have to try find another person first.

The right solution for this is to keep employers out of the skill-based immigration process.