Great question.
The reason there is no drop-down verse selector in the Bible panel is because the verses are already visible in the panel, and the number of mouse movements and clicks required to open and select an item from a drop-down is much greater than using a scroll wheel or the scroll bar in the panel. Also, the Bible panel toolbar already has more controls than any other panel.
If you need to go to a verse without using the scroll wheel on your mouse or the scroll bar (or pressing Page Down with the keyboard), you can click in the Go To Verse box and just type the verse number by itself and press enter. (When you only enter a number, the Go To Verse box assumes you want the verse in the currently visible chapter.)