I agree with pohnpie397 that the two skills have nothing to do with each other and would argue that "blending" the two actually inhibits the writing/ideas skill. When a student is more worried about how the letters are formed than the ideas he/she is trying to express, the teacher is doing a disservice to the student's critical thinking skills.
These are two different things. Handwriting skill is a motor skill issue. The motor skills involved in handwriting are developed by a certain age, and after that point it is difficult to show much improvement. Writing, however, is thinking at its highest level. We must be good thinkers before we can express our thoughts and emotions in writing.
I would agree that it is very important to be able to express your ideas in writing. Many students are uncomfortable with the idea of writing, I think we need to allow students the opportunity to write without the fear of it being detrimental to their class grade. Let them get comfortable to the idea of expressing themselves.
Effective writing is all about trying to convey your ideas to others in the best possible way. Therefore, writing to express ideas would surely make you a more competent writer. The reason for this is that, as they say, "practice makes perfect." The more you write to express ideas, the better you will get at it. This is especially true if you have someone who can critique your writing and help you understand how you can do it better.
As far as handwriting goes, I don't see it. Handwriting has nothing (in my mind) to do with the content of the ideas. Writing is effective because of what words you use, not because of your handwriting (at least as long as the handwriting is legible).