A bureaucrat is specifically someone who is an elected official dealing with governance and policy. A bureaucrat who is an expert in health is exactly who you would want advising on an issue that is primarily driven by the management of a pandemic.
But the reality of it is none of these people are making the decisions, they're advising, your governors are making the final calls. So your governors should have information from economists, health officials and other areas and should be making decisions based on their best judgement of all that information.