I am not in the US and have no experience whatsoever with the actual Everyday Math. But I am studying to be a high school math teacher, and there is a lot of emphasis on the need for literacy to be developed within the mathematics classroom. As mentioned by Aufilia, a lot of mathematical processes can be memorised without actually understanding the mathematics behind it. I did quite well in mathematics all the way through university, but when I try to explain ideas, I realise that I lack a lot of the conceptual underpinning and authentic understanding of why I am doing what I am doing. An example that really drove it home for me was the process of how to divide fractions. I know to invert and multiply, but then to try to think why that process works and how to explain why it works is an entirely different issue. And at a higher level, I took calculus twice, about 10 years between each time. The first time I memorised the process for integrating to find the area under the curve, which worked perfectly well. The second time, I actually developed an understanding of why it works, and this was a much richer understanding.
I feel that my own education let me down by not building a strong foundation in the conceptual understanding of mathematics, and I hope to help my students with that. I didn't find the actual lack of understanding affected my ability to succeed in the mathematics classroom, but does affect my ability to teach effectively. We learn through language, and being able to write the mathematical processes is important, but also being able to explain them helps to develop a deeper understanding of what you are doing.
Word problems are dreaded by many students. They are not always an ideal way of presenting mathematical problems, but students often struggle because their ability to use mathematical language needs further development, not because they do not understand the mathematical processes involved in the problems.
I don't think writing should be arbitrarily thrown in, and students should not have to write down every thing. But I do think language and writing are powerful tools for math learning.
