Of course this seems ridiculous and illegal as public schools have the obligation of educating all children. Some children, however, do fall through the cracks. You do not have to agree. If a teacher or school person approaches you about testing your son or daughter, you do not have to comply. It may be that there is no point.
Testing can be very useful for families and students to learn about the student's strengths.
More information is always better than less, and it does not need to pigeon hole your child. Unfortunately, the school doesn't always catch these problems, or take responsibility for them. Individual states then have the task of writing their own guidelines and training and educating the local school districts, intermediate school districts, teachers, special education directors and so forth. These are the definitions which the State Department of Education uses, in the wording that they use. A handicapped person who has severe speech and language impairment but whose primary difficulty is other than speech and language, is eligible for speech and language services.