> As I understand it (I'm no expert in the field), U.S. policy in regard to China is that its rise to superpower status is inevitable

Interesting. My understanding is quite the opposite: that the U.S. policy in regard to China is that its rise to superpower status is in question.

China is 25 years or more from being on par with the United States in terms of military projection in its own region (much less power projection in distant lands and seas). China has legitimate issues with all of its territories that have strategic resources: its water is in Tibet, its minerals and oil is in its Uyghur region. The United States today has China surrounded by the "first island chain." China's economy is robust, but has inherent weaknesses that could cause it to fracture as it tries to jump the 'middle income gap'. Indeed out of several dozens of states that have attempted jumping the gap, only a couple have succeeded. Ongoing sovereignty disputes in Hong Kong and Taiwan keep the Chinese mainland divided and focused in on its own territory. Japan today could match Chinese military might, and with the right trajectories could maintain an upper hand in the future. America has tried to block Chinese multilateral/international banking efforts (AIIB, ADB, etc) and it's admission into the Special Economic Basket of currencies at the IMF. Today the United States (well, under the prior administration...) is trying to prevent full membership of China inside the WTO, and it's membership isn't guaranteed. India forms a natural check on Chinese regional power as its population is larger than China and its economy is growing at even faster rates. Russia (which shares a huge and important border with China) and America both eye China and it's ambitions and could individually or together align to snuff Chinese expansion where they to find a good justification. China's international investments are questionable, as much of them are in countries with poor histories of solvency (this is a strategic bet on the part of China). It's One Belt One Road infrastructure project is vulnerable to stability issues in Central Asia (of which there is a long history). The people's party in China also (rightly) fears regime change operations in their country - this remains a real possibility. China has a burgeoning nuclear power (DPRK) on its border, a nation in dispute with a long time American military protectorate.

The United States has a lot of issues it can make with China, from internation trade, currency practices, South China Sea settlement, Taiwan and recognition of independence, Japanese security (look at their reform of National Security legislation), Indian bolstering, Korean Unification, Russia's far east, Central Asian proxies, etc.

The United States is hoping that, with containment pressure on all of China's strategic bets that it won't be able to realize its ambitions to greatness - and will fizzle. This is a practiced playbook: it's how the United States prevented the Soviet Union from realizing super power parity. Curiously, the timeline originally predicted by strategic thinkers for the Soviet Union for parity was also "25 years."

Including China into the "rules-based international order" isn't code for "we want a nation as powerful as our own to also rule the international order." The United States Grand Stategy toward China - indeed toward any and every potential adversary - is to prevent their rise by raising obstacles and costs to its succession.