One of the advantages of drop bars is that they allow about five different positions for your hands. The STI shifters used with drop bars allow shifting and braking from two of those positions: with your hands on the hoods (used for relatively relaxed riding), and with your hands "in the drops" (for when an aerodynamic position is needed).
Fitting gripshifters to drop bars isn't very practical, it requires the drop bar to be split in the middle (to get them on), which in turn requires a special stem, and you could only use them when your hands are on top, or they'd have to be fitted to the lower straight bits (impractical).
Fitting Shimano trigger shifters afaik doesn't require the bar to be split in two halves, but they also could only be operated from one hand position on the bars.