If the world used Baidu, it would be a propaganda coup for the CCP. They'd have the ability to disappear information they want to suppress (like criticism of the camps in Xinjiang), and freely push propaganda and disinformation (a la https://en.wikipedia.org/wiki/Operation_Infektion).
Think about it: if the web existing in the 1980s and the Soviets controlled the world's main search engine, the top results for "AIDS" would be disinformation articles about how the US government created it.
So, I'm sure the CCP would like the world to use Baidu, but it might not be high on their list of priorities to push right now.