I went through this as a child, where you do the same problem over and over again. Some of the symbols change, but the operations are identical.
It reminds me of when I was in 1st or 2nd grade doing long subtraction. And I had informed the teacher that I wanted to create the problems for the class, so she let me (on the chalkboard). But I snuck in some problems where the result would be negative. The kids struggled with these problems, but not a single student in the class said anything about the structure of the problem. And why would they? They learned nothing about what they were actually doing. It was a sequence of subtractions and carrys and other magic.
the fact that when done badly it rarely yields insight does not necessarily mean it shouldn't be done.
I'm about to make a sweeping generalisation.
The problem is virtually no one in the world can teach math properly. Those who love teaching kids usually hate math and transfer their lack of skills and negative attitude. Those who really, really understand math are usually the type of people who would never teach 3, 4, 5 year olds.
People end up doing math despite the system, rather than because of it. They can usually point to one specific inspirational teacher. My specific inspirational teacher gave me lots of mind-numbing exercises and helped me find the insights.
Rote learning of mechanical processes will rarely, of itself, lead to anything other than a hatred of math and a lack of understanding about what math is. Repetition of mechanical processes, guided by someone who really understands stuff, and asks prompting questions, can lead to discoveries and genuine excitement and engagement - I've seen it happen.
How will we ever get really good math teachers?
There I have no answer.
Arithmetic algorithms still have value - for the insight they give on arithmetic and because following a complex algorithm is itself a skill with value.
But there is no need, as we do now, to insist on performing them so many times, or to do them very quickly in exams.
The main problem with this new approach, I feel, is that it makes learning mathematics harder. Building richer conceptual models which is necessary for both applications or theory is more interesting and meaningful, but also more difficult than following prescribed algorithms. It is harder to test in an exam, and where testable the problems are much harder.
This issue of algorithms vs conceptual understanding, is important at the undergrad level too. Eric Mazur has a nice video about this where he also talks about his way of testing conceptual understanding by asking very simple but illuminating questions - http://www.youtube.com/watch?v=WwslBPj8GgI
We're so "drill, drill, drill" focused that we lose sight of why we're doing the drills (Eric Mazur calls it "plug and chug"). It's possible that these drills will in rare instances create the likes of a Colin or an Andrew Wiles, but for virtually everyone else you have a group of students that can solve triple integrals, multiple 5 digit numbers in their head, factor matrices into any form desired -- yet not have a clue why.