Not saying this as an defense to your observation, but it's possible that they just don't have the capacity to manage that information, given the disparate nature of our health care system. Others have pointed out that the entire pandemic response org chain was fired a while back under the premise of cost savings.

Communicating that information back in a secure, consistent, and reliable way requires a "system" of some kind. It could be a secure website or even a phone war room ready to go and staffed with operators waiting for the test reports.

If such a system was available, you'd think they'd use it in heartbeat, which kind of implies it doesn't exist.

And it's not like systems of this sort - or more even more complex - don't exist. When my kids were born, we donated the umbilical cord blood to a stem cell bank. The organization sent me special bar-coded packaging with a refrigerated pack to be overnight posted back to them.