Note that getting to the full quick settings UI requires swiping down twice; the first swipe gets you notifications, the second one adds the quick settings. Alternatively, you can do a two-finger swipe down and you get straight to the quick settings. I can't reliably do that with two thumbs (too hard to synchronize the swipes), so that method really does require fingers. But two quick swipes work fine.
On a tablet, the one-finger vs two-finger swipedown makes sense (because it is easier than reaching from the right corner of the screen to the left) but on a phone the right-vs-left makes much more sense because you're more likely to be holding and operating the phone with the same hand (Note: my N5 is broken atm so I can't check the on-phone behaviour).
There are other things I dislike about Android on a large tablet, but the biggest one has been around since 4.0... having the 'navigation' buttons in the middle of the device where neither hand is conveniently close to them.