Because Kaido values King for his combat prowess, whereas he keeps Queen around mainly for his science
A scientist is of no use in a war such as the war of the best, even if Queen is strong thanks to his DF and his science modifications, he's incompetent and is at his best in his labotary
King on the other hand, is much more combat capable, he's also far stronger than Queen too, he's the perfect person to bring to a war, specifically, as a right hand man