You are assuming the meter works on a different principle. Your calculation is measuring the center voltage of a potential divider with XL as the top element and R as the bottom one. It will work but it relies upon a constant frequency and voltage as the signal source and both would have to be selectable to cater for different L and C values. It can be done but it isn't paractical.
Most LCR meters work by applying a step change in voltage to one end of the component then measuring the time delay before the other end reaches a certain potential. In other words it produces a single time measurement which can then be mathematically converted back to the value. The comparator is there to sense when the measuring side has reached the necessary voltage. It's a much easier way to take measurements.
Brian.