Did Communism/socialism prevent China from giving other countries, including the US, a heads-up re coronavirus ?

Yes, the Communist Party of China's need to save face and appear omnipotent ensured that other countries would be needlessly infected by Chinese grandstanding. And now, China is working on disseminating propaganda to downplay their blame for the disease's victims and the Liberal media assists the Chinese Communist Party at every opportunity in their quest to oust President Trump from office, even going so far as to label COVID 19 as "The Trumpvirus." and now the Liberal media is trying to downplay the actual source of the virus, the city of Wuhan.

2:37 PM March 12 2020,  Lijain Zhao, Spokesperson & Deputy Director General, Information Department, Foreign Ministry has just tweeted, without the slightest shred of evidence, that the U.S Army brought the Wuhan virus TO Wuhan. No doubt this will be echoed loudly by the Liberal media which whined "Racism" at the labelling of the virus that originated in Wuhan as The Wuhan Virus.

No, China is quite capitalist.

They could have warned the world a little earlier, but their culture prevented them from doing so

Yes. Communism is a cancer for all people.