I'm not sure I'm satisfied with this answer, but I think it indicates where I am headed.
At one end of human interface design, GNU Emacs. It is so flat as to allow [nearly] complete freedom of expression by the user. The price? The ability to deploy an ad hoc set of abstractions creates the possibility of multiple learning curves and requires a sophisticated mental model to be maintained by the user.
At the other end, maybe something like the sliding rheostat on my toaster. It controls one thing directly and proportionally. It persists across machine states [i.e. whenever I am using the toaster I have direct access] and is functional - a given setting produces the same output (in terms of energy, if not of toastiness.)
What isn't good flat design is Apple's new calculator - or rather it isn't good redesign despite being executed in a flat idiom. It removes functionality by eliminating mc m+ m- mr. The end result is that for aesthetic effect, Apple has made the calculator less useful. It has reduced the user's ability to express ideas.
They have used flat design as a cop out. I am sure that they have data which indicates that most iOS'ers don't even know what mr does, let alone uses it. But the real design question is, what would people use, and the answer is probably something like parenthesis and square root and maybe a doubling function and a halving function and something which multiplies by ten...and notice I've got five buttons that they need to stick in their four column design?
See, this is the problem with skeuomorphism. Apple still wants to make something that looks like a pocket calculator, instead of crating an interface to a general computing device.
What would a really useful phone calculator look like?
I've been thinking that the real future is between, User Interface design and Human Interface design. Is the future of our interfaces going to allow expression or only interaction within a loop dictated by the machine? Keyboard Cat can be trained to flip switches, but cannot express a musical composition. I look at the Apple calculator and wonder, where is the Integral key?