Of course some radars did physically move their dishes to stay locked on to a target. I'm in the middle of The Invention That Changed the World (spoiler alert: it was radar) and I was stunned to learn how well this worked with analog circuits. An SCR-584, paired with an M9 analog computer, could detect that a plane was moving out of the center of its conical scan, and then convert that into a signal to the motors that drive the dish (and its associated antiaircraft guns).