The advantages of gridded battlefields?  Manifold.  

Speed of play. - removing measuring for movement and firing etc. increases speed of play by almost 100%.  

Accuracy - figures are clearly within range or without range, an extra few mm here or there is NOT of critical importance.   

Aesthetics - no more balancing figures on a hill to show EXACTLY where they are,  no more hesitation about putting on the battlefield a wood or marsh because of the mental arithmetic such a terrain item causes in other rules, battle lines that are not too regular or irregular etc.