Provided that China becomes less authoritarian and the US doesn't do something stupid, it's not impossible for both to coexist, while still competing.
The second time might have been interesting for world history, as the French PM proposed it before France decided to join the Treaty of Rome nations to bootstrap the EU.
The issue is mostly China grabbing international waters like the S. China Sea as sovereign territory, grabbing Taiwan, pressuring Japan and neighbouring states, and building what will eventually be a string of military bases throughout East and South Asian oceans.
The US, in comparison, makes sure that everyone - including adversaries like China, Russia and Iran - can navigate the Suez, the Panama Canal, Red Sea, Arab/Persian Gulf, S. China Sea, Straits of Taiwan etc.
There would be zero problems, and US Navy presence in Asia would be minimal if China wasn't trying to hustle this outside it's borders.
And FYI Americans do care about authoritarianism, and there is constant pressure on places like Saudi to reform (and FYI there are steady reforms), though yes, it's very secondary.
The paradox is that China is pursuing a macho 'we're the local king' strategy much like Russia, when for it's own benefit, the military escapades are not fruitful. Maybe in China's case there are some advantages, though almost none in the case of Russia.
The new Belt-and-Road strategy is an example of a good project that will have immensely positive results for most players - shenanigans aside. Nobody is against any of this, we are all for it, except for the shifty things like debt-traps to grab ownerships of ports, which will eventually be Chinese navy bases.
China will continue to pursue the authoritarian entrapment of the citizens of HK and Macau, and of course Taiwan, which isn't good for anyone really.
Right now they do. But if conflict breaks out between China and the US you can guarantee the US will use its navy to block all trade with China. This puts China in a very vulnerable position, which is why they're willing to risk upsetting neighbours by aggressively pursuing bases in the South China Sea (as well as the Belt and Road project).
>>> There would be zero problems, and US Navy presence in Asia would be minimal if China wasn't trying to hustle this outside it's borders.
Why do you think that?
>>> China will continue to pursue the authoritarian entrapment of the citizens of HK and Macau, and of course Taiwan, which isn't good for anyone really.
My wife is Taiwanese so I understand the situation pretty well. I just think it's a mistake to put this down to ideology or democracy versus authorianism. It's just two states vying for power, the same thing that's been going since forever.
In the inter-war years, the UK was no longer concerned with Germany, but, due to the Great Depression, was also too damn broke to go on international adventures. The same situation played out in the US.
The only reason the two powers are now aligned, is because the United States started seeing communism, as opposed to European colonialism[1] as its biggest threat.
The moral of this story is that superpowers can have friendly relationships when they have a common enemy, or no conflicting goals.
An obvious question, here is - what are the conflicting goals of China, and the United States? The answer is - influence among China's neighbours. If the US was not interested in maintaining it, there would be no conflict.
[1] In the 19th century, European colonialism was a threat to American colonialism. In the 20th century, the American empire has resisted de-colonization a lot better then European powers did.
The optics of it were anti-colonial. The implementation of it was absolutely colonial. This is one of the many baffling contradictions of America.
Central and South American states were only allowed to be independent of European rule. They were, and continue to, be client states of Washington. When they forget this, they get regime-changed.
America's 19th and 20th century adventures in Hawaii, the Philippines, Samoa, Cuba, Puerto Rico, the annexation of Mexico's territories, and deportation and repression of native Americans were all colonial power grabs - and all performed under the aegis of the Monroe Doctrine.
This is the fundamental difference between the British Empire of yesteryear, and the American empire of today. The British public was never confused as to whether or not it was at the head of a globe-spanning empire.
There were never "friendly" relationships between two superpowers in history if I remember correctly.