The battleships of the First Fleet - Main Force(Yamato, Nagato, and Mutsu) could have kept pace with the carriers during all but flight operations and evasive maneuvers. As it was, the United States operated their slower battleships(North Carolina class and South Dakota class with their carriers). Further, the Kaga(slowest of the four Japanese carriers at Midway) was only slightly faster than the Yamato, Nagato, and Mutsu. You have to remember that most of the time, the carrier forces were not operating at full speed, but at a cruising speed. As operating at full speed burns up massive quantities of fuel and greatly reduces range.