Why don't all motors burn up instantly?
It doesn't, the motor itself does. Once the rotor starts spinning, the motor produces a voltage that opposes the flow of current; this is commonly called "back EMF (electromotive force)".

The motor's speed increases until the back EMF reduces the current flow to the level needed to account for the actual physical load on the motor (plus losses).

The heavy current you calculate is drawn only for an instant, just as the rotor starts spinning. If the rotor is prevented from spinning, then that current will be drawn indefinitely, and yes, it can destroy the motor.