(I have not yet tested the new UI (hopefully availlable monday?), so this comment is only about the principle, not my experience with it.)

I have not understood why they have gone this way, and don't see why you find it better.
I mean : the OS is designed around multitasking, so having apps opened at all time. So opening apps should happen only sometimes.
On the other hand, being able to check notifications from everywhere makes more sense. I open apps a few times a day, but constantly get notifications about calls, mails,twitts, sofware updates...
Also, a lot of apps are opened as dependancies of other. like the browser when following a link in a tweet from the events view, or the contacts lists when adding a new contact that just called from the call log. So having the 4 most used app as direct shortcut below the home screen was actually good. The other apps are usually opened from these 4 or from the events.

Don't know if it is just my usage, but it feels strange. I will see when the update is there if I get used to it.

It has always felt like too limited in the previous version : It needs 3 buttons to control the media player: back, play/pause, next, not just 2. There is no way to quickly start/stop data or gps in the settings app cover (the kind of simple widgets I had back in symbian). And as the cover are always moving (each time you open an app at the end of the homescreen, it gets back first, moving all others), it takes some focus to search where the cover is to interact with it. It has to be compared to a widget that is always at the same place (the one you chose!), so that your hand can learn to use it without thinking.

In this new version, it is even more limited, and hard to use as you point out (remember all the talk about why buttons suck), but it is not possible to do better due to the changes of gestures for the homescreen.
I can see only one solution: get rid of them totally, and get back to an harmattan like multi-task only view.
The media player controls would fit better in the lockscreen and event screen, the shortcuts for data/gps in the event view. As it is done for months thanks to patches.

I am looking forward to test this in the coming week.