I had my V10 for a little over 2 years and didn't really get used to using the second screen until the last 6 months. NOW, I miss it a great deal. I'm trying to get used the the floating bar right out of the box, but no matter where I put it, it ultimately gets in the way of other apps.
Put it towards the top under the action bar? I keep mine in the middle of the screen and it very rarely gets in the way of anything and, if it does, it can quickly be moved. I only wish you could adjust the transparency and color.
As for second screen use, in the year and a half I had the V20, I pretty much only used the second screen to take screen shots, toggle flashlight, or launch my calculator or camera. Occasionally I'd use the volume toggle, but my volume levels are automated so it was mostly unnecessary.
The second screen would have been far more useful on a smaller phone. It was just too high to be useful casually and quickly unless you just always have two hands on a phone. I use my phone primarily one handed unless I'm typing so it just wasn't as useful as it could be.
It was good for wait it was, but it definitely isn't missed. LG could have done better in terms of functionality. For example, it's disabled if you're using a full screen app (except for the time) and the options for quick settings toggles was too limited (I wanted rotation).