I've helped out in primary classes, and sometimes when I've done something like this kids have been so excited they've jumped up and run around, unable to contain themselves. They've suddenly seen why something works, not just been told to memorize it.
It's the range of ways of thinking about things that matters. Here's one that doesn't work for you. Fine. Find another. Use both. See how they're the same thing, but from different points of view.
Sorry, I'll go away and stop ranting now - I'm just getting angry and will say something I regret.
Another silly thing I read about is associating numbers with animals. So "1" is the crocodile and "2" is the elephant or whatever. I can only say - wtf? Just another example - numbers are numbers, not elephants...
I just think to understand maths is to REDUCE the number of concepts (that's the beauty of maths). A lot of teaching concepts seem to increase the number of concepts instead.
I am not a teacher, though.
It sounds a lot to me from this and other contributions you've made about math that you, like many others, have been damaged by some really bad teaching. Using these techniques properly gives the child/student powerful tools for analysing situations they haven't seen before. Teaching rote techniques doesn't - of itself - provide that power and flexibility.
Having said that, these "illustratory" techniques are often taught appallingly by well-meaning and gifted teachers who themselves have learned by rote what to do, but don't themselves have any real understanding of the math underneath. We need teachers who are gifted teachers, but who understand the underlying principles.
Unfortunately, those gifted in math are rarely gifted in teached, especially teaching children. Add to that the fact that they could earn more respect, reputation and money using the math, and what we have is a continuing disaster in math education.
I have no answers.