very simple, the Chinese supply lines problems and new American/UN reinforcements, along with the lack of support from the Russians means that china was unable to take over the entire south. in fact china being unable to takeover SK against the Us should have been the expected result, i mean china in the 50 vs the US? who woulda thought.
what is incredible however, is that china and once-shattered nk forces was even able to push back from the Chinese boarder and reach a stalemate at the 38th parallel against the US led UN force. heck even being able to sneak hundreds of thousands over the river initially without alarm was amazing, even if at the time there were no drones and sats to watch you.
now as you say most people were against even going north and even fewer would wanna enter china that is true, but even with your "thin" supply line, the American forces were 10 times better supplied than similar Chinese forces which add all the more amazement that we ended up settling at the 38th.
and yea chances of war currently is low to very low, both sides are refraining from sending military forces and are just bumping around with civilian agencies.
even if war broke out though, i dont think it will be as you say, china doesnt plan on invading japan, any war stemming from the island disputes will be a naval and perhaps economic war, at any rates most people would agree that, as things are now, time is on china's side.
In korea war, the US/UN force does not expect a China intervention and the sole purpose of US/UN attack force intention are to push the North back to the North and hence achieve a status quo.
The problem is one man, abeit it is the Militarily Gifted Macauthur. The problem is, he set his standard too high on the get go. Anyone with a mind will know his plan is destined to fail (This is what we taught in the Military Academy)
If you study the troop strength of UN/US side, it is estimated on the date that the Chinese crossing the border, the troop strength is no more than 250,000 and only about 100,000 of those are in the front line to the north. but on that day alone, China rush 300,000 soldier across the border. Which is already roughtly the size of the whole UN Forces Korea. It tip the balance heavily on the Chinese side, when you are facing a logistical problem and a renewed force of 300,000. There are nothing to do but retreat.
The way the Korea war fought is a basic seige warfare and it is not come to a surprise It draw in the middle and right back where you started it. Also, do remember the time of Korean war is the time US Demobbing its whole military coming down from WW2. And majority of the force are stationed in Europe to counter the Russian Threat. The US is literally fighting a limited war in Korea.
There are one interesting point you mention Russia as a factor China cannot go all the way. That is true. If Russian support the Communist KPA/PVA from the start, it will be quite easy for the combine communist force to go over the south. Will that change anything tho? The answer is no. As Russia also being tied down in Europe, the same reason Why America do not use full strength as they done it in WW2. If Russia send any sort of Help to North Korea, they would have somehow left the East Europe open, and to Russia, they border East Eruope rather than Korea. So in the end, they also have to savce their own arse first, then come to help their communist brother.
China, on the other hand, have no such problem, however, because of the Korean war, it gave Taiwan a breather and literally, the Korean War is what saved Taiwan.
And yes, America is better equip than the Chinese counter part. But there are just too many pof them. And they are running out of ammo. Running out of supply is one very big characteric during the whole Korean war. You can fight for a few week without food, you can fight a few day without water supply. But you will not last 10 second if you do not have ammunition.....
GOing back to topic.
Even the chance of Border conflict is small as the island is a lot closer to Japan than to any Major Chinese city (I think i worked out from google map once the closest Chinese city is about 190Mile away, where the cloest Japanese City is only some 100 mile away. It would be an away war if Chinese decided to fight it.
And i do not agree time is on Chinese side as you have to assume Japan do nothing but sit on their ***** and China grow strong everyday. The truth is this is not the actual case. In Island warfare. Time is everything. If you allow time for your opponent to increase defense on an island, time to position their hardware in the island, all this will stack against the invading force.
We all know Japan have the means to fortify the island. But they do not have time to do so yet. BY the time China grow strong, they would have been able to heavily fortify the island. And from all the experience it see, in the end, if you waited long enough, the war will just become a meat grinder as you can only deveople technology like aircraft and missile. But to fight an island war. You need to most premetitve thing in modern battlefield at all, That's troop on the ground. No matter how technological superior you get, when you go and do the dirty work on the ground, you negate all the technology different. I have this kind of experience first hand. Whether you believe or not.
Actually, it ain't funny at all. By the time of the Korean War, US had reached its peak of military power but China had just stepped out of the ruins of 8 years anti japs war and 4 years civil war. Who would expect China alone to defeat US with almost just light weapons? It was a success for China to stabilize the front at the 38th parallel and finally made US to accept this fact.
If Macarthur did not find out Ridgway's talent in west point and Walker didn't die, US may be dragged into a more difficult situation. It is exactly what you mentioned about the stretching of supply line that caused our troop's attack could just keep about a week, and this phenomenon was caught by Ridgway to develop his viscous tactics. As far as I learn, this is the turning point of the whole battle.
More and more discussions about whether we should be involved into that war were addressed and not all of the Chinese support this action because of the large number of casualty, the danger of being attacked by nuclear weapon and more importantly the loss of chance to get back Taiwan. And that's also the most important cause of our dilemma nowadays in Diaoyu Island.
Actually, US was at the bottom since coming out of WW2, we even have difficulty muster 1 division to fight the delay action. Again as i said, we are in demobbing from WW2, and almost all of our remaining military power is dedicated to Europe instead of the Asian Front. We are in no way to fight a war in the whole year of 1950.
Chinese did not defeat the American in the Northern Forntline by the means of light weapon, they crushed the UN spearhead by sheer number. 100,000 may be acceptable for soldier to fight on, 200,000 is the maximum limit, but Chinese send 300,000 in one day. That's in case you don't know, is a lot of people.
The US actually had realise the Supply problem even before we set foot on the North. That why we only send a portion of the troop to the north and thus reducing the problem. However, with Chinese main force trying to stroll south, you are talking about 1 millions PVA + KPA troop. That's a very large army to support and just after 1 year or so, acutally both side already settled the fact that No UN troop can cross the 38th to the North and stay, and no Chinese/KPA troop can cross the 38th South and stayed. Hence for what i concern, the last 2 years of war is just waste of time and human life.