Are they incentivized to do that? Remember they’re dealing not just with The west’s opinion, but also home opinion, where I don’t know that documenting that they should have found this weeks earlier would go over well. Not to mention I think they’re happy with the current local conspiracy theory that this was actually the US’s fault. It also seems likely that a big city especially one with a big lab would be more likely to be able to identify that the disease going around was new
I'm not an expert on China but I would generally assume that the consequences and reputational damage of being seen as responsible by the rest of the world for COVID-19 would outstrip nearly any other possible consequences being mitigated against by not seeking to clear themselves.