What kind of "rules-based" world order should the US be defining (or prooting)?

The foreign policy phrase "rules-based order" is coming under some criticism.

The press and ordinary citizens should always take a critical view of their country's foreign policy, as difficult as that may be, especially in times of open military conflict. It is important to have a competent team running foreign policy. The Trump Administration wanted to get rid of as many competent foreign policy officials as they could. But it's also important to hold all administrations to account for how they do their jobs.

Über-Realist Stephen Walt remarks (China Wants a ‘Rules-Based International Order,’ Too Foreign Policy 03/31/2021), "A ready ability to use the phrase 'rules-based international order' seems to have become a job requirement for a top position in the U.S. foreign-policy apparatus."

As he explains, in the new-cold-war-ish rhetoric of the Biden-Harris Administration, the defense of the "rules-based international order" - apparently the abbreviation "RBIO" hasn't become common yet - is invoked against China. The implication is that China is out to tear down such an order.

But Walt places the (partly) contrasting visions of the two big powers in the context of the evolving world, in which China is now the second most powerful country and what is or soon will be the largest national economy, while Walt's foreign-policy-realist descriptions of the state of the world can sometimes be discouraging, he's also able to look on the bright side and discourages needlessly alarmist narratives:

If Chinese leader Xi Jinping’s loftiest ambitions are realized and China eventually occupies the commanding economic heights of the 21st century, it still won’t be able to take over the world. But such a position will give it a great deal of influence over the rules of the international system, because other states will be less willing to defy it openly and forced to adapt some of their practices to conform to Chinese preferences. Even states that are actively balancing against China militarily may choose to accommodate it in other ways. By contrast, if the United States keeps pace economically and retains key advantages in most of the core technologies on which future productivity depends, then the 21st-century order is likely to favor Washington’s preferences more than Beijing’s.

Here’s the good news for Americans: Undertaking the reforms that will be needed to retain the necessary economic strength would be good for the United States in any case, and it would make sense even if China were weaker than it is today and posed no challenge to the current order. In short, the United States is in one of those happy moments where what is good for the country at home will also be good for its standing and influence abroad. [my emphasis]

On the other hand, there really are economic and ideological interests who prefer wars and rumors of wars over what is best for the country and its people as a whole. Something of which Walt is also very much aware.

Rachel Esplin Odell warns of the risk in the current rhetorical framing of the Biden-Harris Administration in relation to China (Why it’s wrong for the US to label China a threat to the ‘world order’ Responsible Statecraft 03/20/2021):

This rhetoric reflects Washington’s tendency to imagine the current world order as a monolithic, liberal system of mutually-reinforcing laws, norms, institutions, and alliances, upheld by the United States and its allies. In this view, states like China and Russia seek to overthrow this order and replace it with one that is more lawless and repressive.

But this is deeply misleading. No such version of a world order has ever existed, nor has the relationship of the United States — or its adversaries — to the present order ever been so simple. And this misconception is perilous. Vastly overstating the nature of China’s challenge to the current “world order” stands to hinder vital U.S.-China cooperation on issues like climate change, fuel a massive and harmful overreaction in American foreign policy, and in the worst case could force China to assume a more aggressive and revisionist posture than it otherwise would. [my emphasis]

Foreign policy is complicated, in other words.

Recovering Iraq War hawk Peter Beinart also expresses reservations about The Vacuous Phrase at the Core of Biden's Foreign Policy New York Times 06/22/2021:

"Rules-based order" (or sometimes, "rules-based system") is among the Biden administration's favorite terms. It has become what "free world" was during the Cold War. Especially among Democrats, it's the slogan that explains what America is fighting to defend.

Too bad. Because the "rules-based order" is a decoy. It's a way of sidestepping the question Democrats should be asking: Why isn't America defending international law? [my emphasis]

Beinart clarifies that the currrent administration is serious about practical and constructive internationalism:

Mr. Biden and his top advisers recognize that international legitimacy constitutes a form of power. They badly want America's allies - and American voters - to see America's overseas behavior as less capricious and less predatory than the behavior of America's chief rivals. They just are not willing to submit that proposition to any test other than one America writes itself. [my emphasis]

Peter Beinart really does seem to have learned from his misguided support of the Iraq War. (Heather Digy Parton, He blew it on Iraq, but makes sense now: Peter Beinart's thoughtful lessons Salon 06/19/2014)