Your math doesn't work and it assumes an outcome that is more likely wildly unrealistic.
At $20,000 GDP per capita (they're at half that now), which would be a tremendous outcome for a nation as large as China, their national GDP will be $28-$29 trillion. The US economy will be that large in about 12 years.
If we're talking that sort of timeline: 3x US GDP would be $84-87 trillion in 2030. ~80%+ of the entire global economy at that point. Even if you shift the figures out another decade, it remains equally silly and impossible.
You might as well say instead that the US will soon push its GDP per capita up to $120,000 magically and more than offset China's population benefit difference with a continued per capita superiority. That scenario is about equally fantasy driven to the notion of China somehow magically having ~80% of all global economic output.
The US exports more annually than China does. Few people realize that. For China to keep growing like they did in the past, they're going to need to find another planet earth to export the next $2+ trillion in goods to, and fast. Those markets for consumption don't exist. They're already over-producing on a lot of industrial goods by 50% to 100% - such as steel - to artificially prop up their economy. That can't continue. Service economies grow dramatically slower than low-wage industrial economies that are filling in extreme slack, which again points to China having a far lower growth rate in the near future.
Put another way, China's easy growth is long since over. That's why they shifted to massive debt binging to keep the fake growth going, taking on $30 to $40 trillion in new debt in just eight or nine years after the great recession. That's a classic signal an economy is running out of easy growth. Their growth return on debt plunged off a cliff many years ago at this point. And their debt is very expensive compared to developed nations, so much so that for every $500 billion in new GDP they've been creating, they're paying $150 to $200 billion just in new debt interest. In short, their economy is being swamped by interest costs, another classic drag-you-down on growth.
It's so bad, China's central bank has begun talking about muni bankruptcies in the style of Detroit:
"China needs Detroit-style bankruptcy as debt problems remain: central bank official"
https://www.reuters.com/article/us-china-economy-debt/china-...
Now does that sound like a country still in its prime on growth, or more likely near the end of an over-extended growth boom?
And all of that recent growth came at a high political cost: their mercantilist one-sided trade approach has alienated all of their biggest customers, so now the US and EU are locking down China's access (including to acquisitions), further dampening China's future growth potential.
China is just as likely to get stuck in a middle income trap, particularly as their demographics rapidly age and we enter the era of AI + robotics + higher automation (ie their population increasingly becomes a liability). And given what's going on there politically with their new dictatorship, vast re-education camps, the erosion of what little speech & expression they had, becoming the world's most indebted nation, etc - these things point more to a negative outcome than a positive one. They look a lot more like Japan economically right before Japan hit stagnation, than anything else.
Historical question: name all the economically very successful dictatorships of the last 200 years.