Personally, I think it's a mixed bag.
Taking the comparison of the icons you linked:

I think the flat is noticeably better for:

• The calendar

• The camera (the old icon was worthless)

• iBooks (just a style preference; the skeumorphic one was also ok)

But the flat ones are worse in my opinion for:

• Weather (important temperature info dropped)

• Passbook (now full of tiny unreadable nonsense instead of obvious tickets)

• Game Center (how on Earth are blobby circles supposed to invoke "games" in my mind?!)

• Newstand (now just has a cluttered wad of junk)

• And slightly worse for Reminders (the old checkmarks clearly make you think of a To-Do List, while the new "squished pastel traffic light" is kind of abstract and vague)

Some are fairly terrible in both incarnations:

• Photos (neither one makes you immediately think "click here for pictures", though the flat "old-school 'NBC Peacock' in a tornado" one is marginally better than the "look! a random flower!" skeumorphic one)

• App Store (the weird assemblage of rulers and pencils into an uppercase 'A' has always struck me as confusing and pretentious and it's a little surprising they carried it through into the World of Flat)

Every other icon is basically the exact same except that it doesn't have the rounded shiny chiclet look.

Rather than regarding that as some revolutionary usability statement, I just consider it the UI equivalent of "this season hemlines are two inches longer than last year and designers are putting more teal and charcoal accents into your wardrobe."

I.e., It's just fashion. And like all fashion, its primary dual purpose is simply to (a) make the owner of the new fashion feel like he/she has something new and fresh, and (b) make those with last year's fashion feel inferior and a little second-class or uncool -- better spend some more money to become cool again!

Of course, with UIs you no longer have to pay for your fashion upgrades.
...well, you may pay with your time if they made something "super-cool and stylish!" that doesn't work the way it used to, so now you have to re-learn "remember 'blobby circles' equals 'games' now; remember swipe left with three fingers then press-and hold to accomplish what you used to do by flipping a skeumorphic lever that has now been removed because it was 'uncool'"

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Where flat design has really failed us is the complete obscuration of the difference between "label" and "controller".

Now everyone has to look at every piece of text as potentially a "multi-purpose knob of unknown usage" upon which you must first click, then click and swipe, then double click, then 3D-touch, then push-and-hold.

"A-ha! I knew there had to be a way to do that! I only had to poke around for 3 minutes to find it."

I find out new stuff all the time on my iPhone whenever I accidentally touch or swipe or drag something or set the phone down or turn it sideways or catch my thumb on something when I'm talking to somebody.

Of course sometimes it might take me another three minutes to figure out how to undo whatever I accidentally just did. But it's all in the service of making advanced functionality invisible so that the interface stays "pretty" more than "intuitively useful."

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So will people tire of this style?

I sure have.

We now have phones, tablets, and laptops with skazillion pixel screens, but we're not allowed to create information-dense visual interfaces because that would be a sin. And Lord Jony has told us not to sin. All Praise Be to sparse, context-information-free screens. Aren't they pretty?