I have a Nexus 10 with Lollipop on it and I really don't see the complaint, at least not the one mentioned in the summary.
Yes, the two swipe-down menus have been unified... but you can still swipe down from the edges to get at it, and in fact you get all of the functionality that used to be in the left and right side swipes from either side now, which means you can get to all of it even if you don't have a hand on each side. Or you can swipe down from the middle. After the unified menu comes up you have to reach over to it with your thumbs to operate the controls and I suppose if you have very small hands that could be an issue. I just asked my wife to try it (she has small hands) and she can reach everything with a thumb while holding it two-handed. She does have to move the thumb hand, but it's a pretty natural motion that doesn't require letting go of the device.
I'm not saying there isn't substance to the complaint, just that the example quoted in the summary isn't really an issue.
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 related note, I like that it works exactly the same from the pre-lockscreen (pops up when you press the power button to turn on the display). The pre-lockscreen shows notifications (whether sensitive notifications can be seen on a locked device is configurable), as though you'd swiped down once, then another down swipe brings up the quick controls, without unlocking. I especially like this when I'm reaching for the flashlight on my phone; no need to unlock, just hit the power button to wake up the screen, then swipe, tap and there's light.
(Disclaimer: I'm an Android engineer at Google, though I work on the low-level security subsystems, not on UI, and have no problems criticizing changes I don't like. I have found very little in Lollipop that I don't like, however, and a lot that I really do like. My only significant complaint so far is the fact that the encryption by default means that when the device boots it can't read any of the storage until you enter your password to unlock it... including any alarms you have set. This means that if your phone/tablet randomly reboots during the night (rare, but it does happen), then your alarm won't go off. This hasn't bitten me, and I doubt it will, but it's not good. On the UI, though... when I go back to a device with KitKat it just feels clunky. Wow, this turned into a lot more than a disclaimer.)