Lack of focus can be due to receptive language deficits (among a host of other things) and not interrupting is a social language skill. That is what a speech pathologist has to do with those things. Special education professionals don't exist in a bubble. The teacher is probably relying on the speech pathologist's expertise with typical vs. atypical child development.
Initial evaluations are comprehensive by law and include at least a screening by the psychologist or special education teacher in all domains (cognitive/ academic, social emotional, communication, motor, adaptive). It gives a much better picture of the child's strengths and weaknesses.
Independent evaluations are great, but in my experience, parents use them more to help identify or explain issues that the school is denying. Getting services from the district can be a challenge.
Bear in mind that much of what is expected of Ks in terms of academics and behavior is developmentally inappropriate. Many 5s can adjust, but many cannot. 5 year old children are not supposed to be ready to sit all day and read and write proficiently. They still should be learning through play. It's too bad, really.