The underhook is not the best way to move your opponent around. There are better ways just for that purpose.
If you can get underhook, you no longer need to move your opponent around. You are there already. When you are in underhook position, you can do a lot of throws such as hip throw, leg block, leg lift, leg twist, spring, knee seize, inner hook, outer hook, shin bite, inner heel sweep, ... You don't need to depend on your single leg any more.
You use single leg when you are facing to your opponent (non-body contact throw). When you get underhook, you can turn your back to your opponent (body contact throw). You have just entered a different door that will require different tools from your toolbox.
Most (not all) of the Chinese throws are to "use your arms to control your opponent's upper body and use your leg to attack your opponent's leg/legs". Since your leg can now reach to your opponent's leg/legs when you are in underhook position, you no longer need to use your arms to reach your opponent's leg. It's time to apply your "leg skill".
One of the "outer hook" leg move used in underhook can be seen in this clip:
http://www.youtube.com/watch?v=_eVGBLUSHf8