A Yonko, one of the pinnacles of strength in the series, getting beaten up so badly that they run away would be the worst written plotlines in all of fiction.
And yet these are the words that came out of Kaido's own mouth
Kaido believes Pirates run away when shot gets too desperate. He said this.
Unless you believe Kaido thinks himself ABOVE HIS OWN definition of pirates Or you think Kaido doesn't even see himself as a pirate, then this is on the table.
This is what Kaido believes pirates do UNTIL stated otherwise
So my theory is based on what Kaido believes. And since I'm a reader and I know that Kaido will lose as per the rules of this story, then according to what Kaido said, he will run away. He says so himself