Can the OP speak Mandarin? Are they familiar enough with the Chinese medical system? This has to be a consideration to purchase or not purchase insurance.
I found in emergency rooms, the doctors treat you differently if you have travel insurance. They can charge for everything, all the imported medicine, ask for any tests, get full price for everything thus the care you get is better than without. There is no need for the doctors to come in and ask which do you want, since money is not a consideration they just give you the most expensive. (not necessarily the best)
Especially with serious illness or accident, the doctors, at least in the smaller cities, expect "Red Envelopes" for good care. I have had first had experience with this 3 months ago. They come to you and tell you prices, this is how much, this is what they have to do, the cost is.... The doctors not necessarily fluent in English albeit most can read it. Under that kind of duress, insurance is really big help.
After saying that, our travel insurance policy is about to end next month and we will not be renewing. We feel we can get by without insurance.
However as for the OP, going to China as a family, sounds like a once in a lifetime vacation, what is a few hundred extra bucks for peace of mind?