Look at the Iran-Iraq war for the level of casualties that some potential enemies are capable of taking (half a million fighting age males dead on Iran's side). North Korea having 9 million military age personnel brought up in a personality cult. Let along China and the size of their armed forces.
The USA lost four thousand in Iraq, two and a half thousand in Afghanistan. The UK lost nineteen thousand men dead on the first day of the Somme in 1916, do you really imagine a Western nation losing that many for any conflict today? To be honest even in a war of national survival I doubt it.
We lack the political will to sustain conventional war. The military knows it and acts accordingly.
Your reply seems focused on the quantity of soldiers. This is an important factor, but I was primarily considering overall spending, which obviously includes lots of capital expense, logistical stuff, etc., aside from the personnel. I believe that the level of investment in military hardware and the like is significantly higher than would be required for a successful war on two fronts (assuming that there exists such a thing as "successful war" these days).
It's why the Iranians had over 1 million casualties taking on Iraq. And several years later, the US rolled over the Iraqi military with 1,000 causalities.
So sure, the US can't successfully invade China, but it would sink the entire Peoples Navy and defend Taiwan, Japan and S. Korea.
We don't do that anymore... Because a full total war is too expensive -- when the US suffers a loss of 20,000 men in a day, a button will be pushed in a silo somewhere and cities will vaporize.
That's why North Korea exists today.