Meh....does it work? If "new math" is resulting in better math skills down the road, then by all means teach it.
Sure, it's weird to me, but that's because I learned the old way and now my brain is stuck that way.
I remember reading something about how a bunch of teachers were "taught" to do math operations in base 4 or something, and they were getting super frustrated because they had never dealt with it before...well, that's how your students feel about base 10.
Again, if the evidence is that this way is better, then I have no problem with it. I certainly use somewhat-similar rounding tricks in my own mental math, and "counting up" has long been a way to reduce mistakes for cashiers.