Regarding training, I mean that it may be dangerous or inefficient to go out to sea too much at such an early stage when they probably didn't even have a chance to test their theory written manuals and basic procedures yet, let alone revise them under a little bit of practice at sea (which is what I suspect they've been doing over the last year).
And of course, it takes time to translate that experience into something which superiors can use to develop into more concrete standards, procedures and doctrines (which is what I suspect the sailors would've been doing when the ship was dockside).
Once they have a more refined idea of how they want to operate the ship, they would probably go out to sea much more, and that is where training comes useful, because they can actually have some standards and procedures to practice with, whereas in earlier stages they'd be going at it almost blindly.
Of course, the above applies to the commissioning of all new classes of ships, but recalling the PLAN have never operated a carrier before (nor any ship with such a large flight deck), and that they have little to no foreign help, and that the ship itself is of an untested class with equipment developed by a nation with no previous experience in carrier subsystems, I think their current rate of sea going is in line with expectations.
It would be nice if they were faster, but at the same time I doubt they have been spending their days dockside twiddling thumbs.
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Putting it another way, the USN have had decades of carrier operation to develop tried and true standards, procedures and doctrines, which allows them to train their crews and go out to sea often with knowledge of what is right and what is wrong and what the yardstick of performance they need for their ship.
The PLAN is at the early stage stage where they probably are only beginning to understand what is right and wrong and what they can expect of their crew. Once they have that down, I expect more vigorous training will follow.
In some ways, the liaoning is indeed an experiment and test ship at present.