CCP's not going for moral high ground because it has no moral high ground. Chinese government always complains about unfair treatment and western media hypocrisy. The term "whataboutism" is also thrown at the CCP whenever western countries criticize their human rights. For example, western countries criticize China's human rights. China brings up things like the Iraq War. Western countries complain that china is use "whataboutism."
This is a Chinese official baiting Morrison, and he didn't need to take the bait. It's a politically-motivated drawing. It might be distasteful, but it is that. Australia didn't need to respond, but this brings up a tit-for-tat that ultimately benefits no one but will be used by China for a global audience. See the types of responses they can come up with to both Morrison and CCP's critics:
1. "Why do westerners bring up China's human rights when their own actions are under the microscope? Isn't that whataboutism? If China can't criticize Australia's human rights, why can Australia criticize China's? If any country with skeletons should keep quiet, then shouldn't countries like Australia also keep quiet?"
2. "Morrison using "outrageous" and "ashamed" over a political drawing? Aren't Westerners about freedom of speech? If only Morrison was so outraged and ashamed about the report."
There's literally no point in engaging. Morrison should've just said: "We don't condone the use of this drawing/fake image, but if it's deemed free speech, so be it. That's a concept that my colleague in China's Foreign Ministry should think about. In the meantime, we will continue investigations with due process and rule of law."
Rise above the bait, and use that moment to show leadership. Instead, getting into this tit-for-tat is pointless. There's no upside to engaging what is basically Trump-esque political trolling.
On your comment on people believing MSM and Big Tech manipulated the election? A political drawing is not the same thing as conspiracy theories on Coronavirus. Nor is it promoting a Qanon conspiracy about cabals controlling people. Nor is it spreading false information about voting for the general election. Twitter not censoring this image doesn't mean that MSM and Big Tech are manipulating anything, especially since "MSM" such as Fox News and "Big Tech" (Facebook, Twitter, and Reddit) are literally where right-wing talking points were spawned and cultivated. People can feel all they want that MSM manipulated the results when the reality is that Fox News and the rest of Murdoch empire, many of which spread conspiracy theories (see Sean Hannity and Tucker Carlson), are literally some of the most-watched/read news networks.
Free speech has gotten tricky with technology, I'll give you that. Certainly a slippery slope for Big Tech going forward.