Here is an article that may help you understand the value of learning base 10: https://mathteachingstrategies.wordpress.com/2009/04/02/big-idea-the-base-ten-system/
As for what's wrong with learning the value of 9+6, nothing, except memorization isn't really learning to think. A monkey can be trained to memorize and respond with the correct answer, but they are not able to take that memorized information and apply it outside of the context in which it was "learned". The new system focuses on teaching children how to approach a problem and use reason and logic to solve it. Your example is for young children, so it looks absurd because of the simplicity of the equation. Apply the same method to 15 digit addition sets and you can start to see the value. It isn't fundamentally different than 9 over 6 "carry the 1", but it more clearly teaches "why" you "carry the 1". Memorization takes a long time to teach/learn. Children these days have to learn a great deal more information than you did before they reach college. Advanced mathematics aside, just the technical info they have to know to do their homework is astounding. My 9yo nephew had to repair some registry errors (on the tablet his school issued him) last week just to submit his assignment. Teaching them to think a problem through is faster and more valuable than teaching them to regurgitate number sets.
As for the basis of this thread, all you really need to know is that there has been a fundamental shift in the way the younger generation views work. You old guys were raised to view your work as a defining part of your character. Work hard, keep your nose clean, and everything will be fine. This generation was starting/preparing for their careers right as the rug was pulled out from under them by gen w/x. They watched as their parents nest egg, house, and retirement accounts vanished due to the poor decisions of borrowers/lenders they don't even know. What then was the value of Dad's 70hr work weeks if you can lose everything (including Dad's job) because of "market forces", outsourcing, and globalization? Your generation lived to work, theirs works to live. They would rather enjoy life than strive for a future enjoyment that may never come. Welcome to the global economy. You old guys can resume your war stories about how nobody works as hard as you did.
Good post, thanks for the article. Pardon me if I m not perfect, it was 60 years ago, but as I remember it we got most of that'grouping' and it was valuable, but worthless if one didnt have the fundamentals of adding/subtracting/multiplying/dividing. And Ill agree that with out an understanding of base 10 its tough I dont think that was the failure though. It was from not enough study on the student. I finally got a real grasp on base 10 later on when I encountered the metric system, much easier to use than ours.
As to your second paragraph, I think a healthy balance is most important.