Problem with that idea is geography.
Just look at the massive headache Syrian refugees are causing all of Europe and the violence and unrest the conflict had fuelled in Turkey.
The golden rule of life also applies to countries - don't shit where you live.
Even if China can contain the war to NK only, it will still face a flood of refugees coming into and either a conquered US client state stuffed to the gills with US troops and bases, or a chaotic failed state on its boarder.
The US has a long and proud history of walking away after creating a giant mess militarily. That mess would be China's problem afterwards.
It would not bog down the US or drain its resources or power, quite the contrary, it would become a source of instability that China would eventually be obligated to sort out.
I can see China being happy to help manoeuvre the US into fighting a pointless war with one of America's land neighbours. But to invite US military action in Korea is to go looking to create problems for yourself.
The only viable military option with NK is total conquest and complete nation building afterwards. Anything less will just make a bad situation worse.
China has no intention of investing the time, resources and blood needed for such a massive undertaking. And no one else has the capability or willpower for an undertaking on that scale.
As Iraq II showed, without a viable post conflict exit strategy, it is pure folly to charge into a war.
Oh you better believe that the CCP and the PLA have been preparing for a devastating conflict in the Korean peninsula for the past 60 years. The post conflict exit strategy is simple, it's massive rebuild with Chinese expertise and Korean money. The two nations have much more stake in the stability of the north than any Western power did in Iraq, it'll get done. China has plenty of reason to undertake this massive task--it's China's last unstable land border region and an unstable regime that's becoming increasingly hostile toward China is about to acquire functional nuclear weapons with the ability to deliver them to Beijing.
If Kim is willing to defy Beijing even in his current situation, what makes you think he'll be more controllable or useful to China after he acquires the ability to nuke Beijing? That's a situation that ABSOLUTELY cannot happen, and China is willing to do everything it can to prevent that from happening. That China seemingly has convinced the world that it's mainly someone else' problem is truly a testament to the adroit diplomacy the Chinese leadership has conducted over the past few decades.