The Chinese consider themselves to be in competition with us -- at War if you will. It's not a shooting war, but a War just the same. There's value in putting it in the US Navy's head that they can't safely push a carrier battlegroup into Taiwanese waters should a real shooting war start.
Frankly, I think the sub was sitting nearly motionless in restricted waters having been alerted to the possible track of the CVBG. Then they just 'pop-up' when the get the acoustics in stereo. Let's see if they can do it in deep water or without their satellite 'eyes'.
There is no value is advertising to your opponent that you are capable of sneaking into the middle of your task group undetected. That would be like the Japanese moving their fleet to within 200 miles of Pearl Harbor and then sending a radio message announcing that they're here. If the Chinese are certain that someday they'll be in a shooting war with us over Taiwan then it makes more sense for them to practice taking out the carriers and remaining quiet about their success or failures.