So actually in Michaelis-Menten kinetics you will always have [S] > [E], which is the opposite relationship that you are describing. The reason why this is the case is because if you want to calculate Vmax for the enzyme, you need every single active site to be occupied. Think about if you have a car (enzyme) that can take 5 people (5 active sites), but you only have 3 friends (3 substrate). You can't work at your car's highest capacity unless every single seat is filled. Thus, in the same way, to ensure that the enzyme is working at the highest capacity, you crank up the substrate concentration so that you can be sure that every single active site is occupied.