My understanding is this is rooted in the perception of hot water as a luxury—it's not like we have any shortage of evidence from chinese texts that people have always drank cold water. The idea that most people even could avoid cold water is an artifact of the last two centuries. Even where boiling water was necessary water was boiled and stored (that's not specific to my knowledge of China, that's just an observation from multiple different places and times).

Of course I'm open to be demonstrated wrong.