What makes you think they don't do that? Of course they do that. They even send chinese women to seduce lonely pathetic FBI/CIA/etc officials to get information. There was a huge story about it a few years ago.
But everyone does it. The brits, french, russians, koreans, japanese, germans, saudis, etc all do it. Hell the nation with the largest spy network in the US is our ally Israel.
The chinese are amateurs when it comes to spying on the internet or in the real world. Once they get to israel's level, then you the media won't even report on their spying and if they do, they'll make excuses for it.