The manga explicitly tells us how Shanks stopped Kaido, they fought, what we forget to ask is what sort of fight was it? A full blown or a skirmish? We’re told exactly what sort of fight.
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Shanks and Kaido had a skirmish – not to sound condescending, but a skirmish/scuffle is a brief exchange, not a full-blown battle. It doesn’t say Shanks defeated Kaido, just says they had a skirmish. The Emperors are individually extremely powerful, a fight between them would likely last hours at least. Could very well be days. They didn’t have an all out battle, but a skirmish.
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Then we have to ask what was Kaido’s goal?
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His goal was to go after Whitebeard; Crocodile tells us that Whitebeard going up against the entirety of the World Government was the only opportunity to defeat Whitebeard – next chapter, Kaido coincidentally gets into a skirmish with Shanks implying he was attempting to take this opportunity too.
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Even if we go with Kaido defeats Shanks in a fight, it wouldn’t be a short fight. By the time the battle is over, Kaido would be weakened and the entanglement between Whitebeard and the Marines would have ended.
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Putting all of these factors together, there was no point for Kaido to fight Shanks for a prolonged period because he’d still not have achieved his goal because Shanks was not going to get out his way unless Kaido wanted a full blown war between his crew and theirs.
*Theory by HPsyche