Some of the 'design' concepts represented by drop shadows, borders, and text-shadows are about function, not (just) aesthetics and when you remove those functional parts of a layout you are left with a less usable layout.
Personally, I love the minimalism and rationalism in the design approach of Dieter Rams, who is (now) considered the father of the design style that Apple has made popular. I also love colour planar imagery (flat sections of colour) like vector illustrations and iconography.
The problem with how many people are implementing this flat style in UI is that we're letting go of valuable information that makes software and websites usable in the first place. This style works great for static pieces (like print, or screen graphics that don't change) and of course looks clean and gorgeous in non-functioning Photoshop mockups - but when you get this style onto websites and into apps it's often done in a way that just falls flat of its full potential.
There's my 2¢. I've been lusting after minimalism in design approach and dying for when colour planar aesthetic style became popular, but now it's here too many people are doing it all wrong (even the big ones, like Apple with iOS7)