I think these letters of recommendation are very important to the student. I don't know about how important they are to college admissions personnel -- I suppose it's different for every college. But students get a real confidence boost when teachers write glowing recommendations.
Both of my sons chose their references very carefully. They chose teachers and counselors with whom they had had great rapport and in some cases not even stellar academic performance. They chose based on academics also -- but ones who wrote about their character were just as important if not more so than the ones who wrote about their academic achievements.
And all the teachers send copies of the letters to my sons -- who were thrilled to read an "objective" view of their accomplishments in those teachers' classes.