Trump couldn't put a doctor or other scientist in charge. Obama would have.

Imagine Trump putting someone in charge who wasn't a knees-bent, ass-kissing servant. Yep, you get the picture. The doctor or scientist might not (probably would not) say what Trump wants said. They'd be bound to stick to the facts and the science. Thus Pence.

The fact that Trump is a constantly lying asshole means he can't have anyone competent anywhere near power, even in a potential national health emergency. The competent and honest might turn against him. That's something he won't risk.

Obama would have had a top notch scientist running the whole thing. And it would have been to Obama's credit.