I'm afraid it is more complicated. There is a thing called "performance legitimacy in China." The CCP has to deliver both material and psychological (ideational) benefits to the citizens in order for the citizens to identify positively with the CCP's political goals. However the CCP is managed by human beings, and humans make mistakes. The worst mistake would be to make a small mistake, refuse to acknowledge, and subsequently cover up when everyone already knows. When such behaviors become standard practice within a bureaucracy, that's how you lose your credibility as a ruler.
I'm afraid you are applying your set of ideals and imagining events based on them. The truth is that the CCP has done so well that it has more than enough credit to weather small mistakes, or even larger ones. When your set of concerns comes into play would be if China's large goals are failing to be met and China looks like it will be fading like the Soviet Union. People may bitch and moan but actual support and approval of the CCP is incredibly high along with nationalism. Right now, if every government that made a small mistake and tried to cover it up were to lose legitimacy, there would be no legitimate governments left, and that's not to say that Beijing will not take responsibility to those 8 doctors; depending on what actually happened (how wrong/right they were and what their methods were), Beijing may well choose to honor them, but now in the heat of battle is not the time.
It is so minor that WeChat and Weibo blew up with demands for freedom of speech and blames toward Wuhan government for cover-ups and delayed response.
What can I say, when a giant walks, people think it's an earthquake. You think that's major? Because you don't know the scale of China. This is minor, and it will blow over into nothing. Wait and see.
The problem is that he was not proactive at all until it became clear that there is a pandemic.
First of all, it's an epidemic, not a pandemic. Secondly, why don't you try being educated in viruses and write the CDC protocol and when something causes undue panic or if an epidemic is not recognized early enough, everyone drag your body out on the street to be tarred and feathered, huh? You want everything perfect with no problems, go do it yourself.
Wouldn't that lead to even more cover-ups and risks of power abuse? Transparency is what compels bureaucrats to do their jobs. Yes, intelligence agencies and the military may require certain degrees of secrecy due to defense against spies, but not municipal government.
The key is competence. The more power you put into the hands of a competent government, the better the result. The more transparency and checks are demanded of an incompetent government, the better the result. There is no government out there as competent and result-oriented as the CCP. And it's easy to nitpick on specific instances where mistakes were made like this one, but overall, my statement stands.