Well, is there anywhere else in China other than Wuhan that could/would identify a new virus like this before it goes mega-exponential?
AIDS, for example, only got flagged because a normally extremely healthy group started appearing with diseases associated with the very old and failing immune systems. And, even then, it took quite a while to figure out that it was a virus.
In the middle of flu season, COVID probably wouldn't flag until your hospitals suddenly fill up for no reason. And even then most people would just write it off as a nasty flu. Otherwise, COVID is just a fairly invisible bump in your mortality rates for people with comorbidities and age. Do you really think China is gonna look too hard into a few extra old and/or sick people dying for some reason?
Given that a full hospital is likely to be the first point where someone will start looking for cause, that really has no relation to origin point.
And, I would argue, China is worse than that. A local party leader in China will absolutely not bump something like COVID up the chain until absolutely forced to. It is quite possible that there were other flare ups that were covered up and the Wuhan one was simply large enough to be uncontainable, close enough to a virology lab to get flagged, and occurred right before Chinese New Year which forced a government response.