They were a little slow to get the mandate in place, and they were a little slow to rewrite the mandate. (which is what should have happened) That didn't make it less valid. You are more concerned with the rights of a few, than the welfare of the whole. That is not how it is supposed to work in times of emergency. The workers as a unit, would have been at work more of the time, and the workers as a whole would have suffered less in their healthiness with the mandate. And more work would have been accomplished for the people. In a time of emergency that is more important than 50 or a 100 workers being out of work because they refused to obey the mandate. Their irrational fears of vaccine's caused this to become a much bigger deal than it should have.
At the time the mandate was written, there was no proof it didn't stop the spread, so rewrite the mandate to include this rationale, instead of eliminating the mandate. The reasoning stated in the mandate was determined to be a violation of rights, but that doesn't mean it couldn't have been restated for the purpose of increasing the government work force. We didn't know that it lessened the effects and the length of the illness when it was written either. But a third of the people were so up in arms about it that they wouldn't have accepted that rationale at that point either. That doesn't make that rationale wrong.
People's rights weren't trampled, the rationale just wasn't inclusive enough to meet the standards of the courts. It could have been, and should have been.