Over the weekend, Sen. Tom Cotton (R-Ark.), one of the most strident anti-Chinese voices on the Hill, argued that the thousands of Chinese students given visas to attend U.S. universities should be restricted from enrolling in science and technology programs. Instead, they should be allowed “to come here and study Shakespeare and the Federalist Papers, that’s what they need to learn from America,” Cotton said. “They don’t need to learn quantum computing and artificial intelligence from America.”

Chinese officials, meanwhile, keep stoking coronavirus counter-narratives. On Monday, the Twitter account of the Foreign Ministry spokesperson reiterated claims that the Trump administration is participating in a coverup and obscuring information about how the virus spread.

Also in a tweet, Hu Xijin, the editor in chief of the Global Times, an English-language state-run tabloid, argued that China is reckoning more responsibly with the virus than the United States, whose “ambitious politicians” are willing to risk the lives of the public by opening up the economy sooner than public health experts think wise.

Observers elsewhere are not impressed. China pursued “very authoritarian measures, while in the U.S., the virus was played down for a long time,” German Foreign Minister Heiko Maas said in an interview earlier this month with Der Spiegel. “These are two extremes, neither of which can be a model for Europe.”

Some European critics have bemoaned President Trump’s divisive management of the crisis and abandonment of global leadership amid the pandemic. Nathalie Tocci, who advises E.U. foreign policy chief Josep Borrell, has likened this moment to the 1956 Suez crisis — an international standoff in Egypt that is remembered as an inflection point in Britain’s decline as a global power. The 2020 pandemic may one day represent the same for the United States.

China, though, is hardly filling the void and may not want to — an argument often ignored in Washington, where an emerging bipartisan consensus casts Beijing as America’s inexorable 21st-century great power competitor. “China has no desire to run the world in the way the Americans or the West have done,” former Singaporean diplomat Kishore Mahbubani told the Asian Nikkei Review. “The Chinese are happy to play their part, but most of all want to take care of China.”

No matter the talk of a new “Cold War,” the pandemic is a reminder that, for much of the world, neither American supremacy nor a newfangled Pax Sinica hold much appeal.

True, for nationalists and populists elsewhere, China’s fiscal clout and growing political muscle does provide a counterbalance to the liberal system once championed by Washington. “Leaders, and populists especially, now increasingly see partnership with the United States — once viewed as an indispensable pillar of foreign policy — and its Western allies as overly constraining,” wrote scholars Alexander Cooley and Daniel Nexon in Foreign Policy. “For example, (the Philippines’ Rodrigo) Duterte, (Turkey’s Recep Tayyip) Erdogan, and (Hungary’s Viktor) Orban all came to power in states that were fully integrated members of the U.S.-led security order. All three now point to potential security relations with Russia and China as providing the possibility of greater balance with, if not outright exit from, that order.”

But even skeptics of the Pax Americana aren’t eager to see it supplanted by the Chinese. “Like Beijing, the U.S. leveraged its pole position in the global economy, its military and industrial strengths, and its technological supremacy to build a world order that responded to its interests,” Indian parliamentarian Jayant Sinha and Delhi-based scholar Samir Saran wrote in a piece that forecast a less free and open post-pandemic world. “There is, however, no equivalence between the two. U.S. society was largely open — individuals, communities and nations from around the world could engage, convince or petition its institutions; write in its media; and, often, participate in its politics. Its hegemony was constrained by a democratic society and conditioned by its electoral cycles.”

“U.S.-China cooperation has been almost entirely absent during the early stages of this crisis, which now seems as likely to deepen the two nation’s divisions as it is to bring them together,” wrote James Crabtree in the Asian Nikkei Review. “The aftermath of the global financial crisis suggests countries facing recessions and anxious domestic populations also all too often resort to protectionism, worsening both their own economic circumstances and those of their neighbors.”