I'll definitely want my country's Secretary of Health to be a doctor who understands public health and its related policies, not a politician whose primarily skill is being popular and getting elected.
>The main qualities needed is being a good manager and able to listen to alternative views and being a good politician.
A Health Secretary who's not a doctor would find it difficult to judge if they're being fed the right information by their advisers.
Remember that Boeing's woes began when the company ceased to be run by the engineers and aviation experts, but instead by the arrogant MBA counters who likely pitched themselves as good managers. It turns out they mostly cared about management and printing cash, but lacked engineering expertise, leading to screwups like the 737 Max.