It needs customization to modify existing styles , also apart from dropdowns we have autocomplete,button behaving as menu where standard is set to show the arrow marks to right side.
Modifying any one of them again requires changing styles for each control that looks like dropdown, so that application wide fixed standard can be used, which adds to complexity maintaining custom styles.
Many users don't target with the mouse, and when in doubt, the most predictable solution is to leverage the familiarity that using standard controls breeds.
I would highly recommend not to change the position of dropdown arrow as this may result in some cross browser compatibility issue. However, if you want to implement in anyway, you may use the below CSS style.