I think the problem with how these new concepts are presented, is that they are taking these ad hoc methods of doing arithmetic and trying to turn them into algorithms. My guess is that this is driven by the need children have to know how to get the “the right answer.”
The traditional algorithms aren’t very intuitive, but they work. Trying to make an algorithm out of the various ways you can break up a problem, ad hoc, seems bananas.
There are systems for doing rapid mental arithmetic. The Trachtenberg system is one that I played around with at one time. [1] I'm not sure how useful they are though outside of needing/wanting to do more rapid calculations in your head.
I found it a huge boost to my ability to do computations without paper or other tools when I learned it in elementary school; I think it's valuable, but I'm not certain that the manner in which it is often being taught now is helpful (which, AFAICT, is not so much a matter of the Common Core standards as poor curriculum attempting to implement the standards.)