Ok I will try my best to explain this the best from both what I have learned and what I have in terms of experience.
The need for alternative schools is due to the fact that each student is unique in terms of the way they learn. You are correct for a vast majority of students the traditional model of school suits them just fine. They go to class everyday for four years and at the end of that four years they receive their diploma. There is however a group of learners that do not or cannot utilize this model of school whether it is due to phisical, mental or other factors.
In its most basic sense an alternative school is any school that does not follow the traditional model. There are a wide variety of these in the US today. I gave a few examples of them before. There are academies for sports, music, the arts and even technology and science. Julliard would be a great example of this. It allows students to focus on the arts along with focusing on their history and english. You can't get that in a traditional school model.
Going back to my student that is attending a ski academy out east. His daily schedule will consist of working with tutors for completing my schools graduation reqirements, along with taking coursework there, along with having blocks of time during the day to practice and take advantage of the weather. His main link will be email and a laptop. Aside from his skills in downhill skiiing he is no different than anyother kid in terms of learning capability. He would not be able to exist and train in a traditional school model.
Next I have a buddy who has a daughter that is totally blind. He is sending her to a school that specializes in children with vision disabilities. The school is totally normal in terms of curriculum but also infuses cane training and brail with their every day activities. Likewise his daugter is "normal" in terms of her abilities except she cannot see. Actually I would be able to go out on a limb and say she has above average intelligence. Once again would not be able to exist in a traditional school model.
You mentioned a phrase before - "special needs" - that I think gets really misused by people outside of education. I honestly believe that there are some people both parents and students alike that abuse and mislabel themselves all the time. I would love to get rid of this term all together but there ARE certain students who benifit from special education. LD, EBD, CD kids are in our schools and have every right to be there by law and no one can deny that they need special services to co exist with mainstream kids.
Another thing to think about is the fact that home schooling, charter schools, online schools, GED programs, and any of the other programs out there are all by defintion alternative schools. You cannot tell me that all of the students in these programs are prime examples of the labels you used before.
From the sounds of it the district you went to had a seperate school where they sent students that needed more attention, a "safer environment", or better services than what could be offered at you individual high school. I honestly believe that this is a great idea. Why wouldn't you group this portion of a high school population together to better serve them? I saves on money for the district by centralizing it, gives the students more access to people trained to teach them and it allows for a better chance at success. Most of theses types of schools have strict admission requirements for enrollment usually requiring testing and an experts referal. We don't look at a student from a Julliard type school in a negative light do we? It's the same concept
If we did not have these schools I am willing to bet we would have alot more of these incidents and drop out rates would be higher than they already are. To label these kids in a negative light is both dangerous and adding to the problem. My district is currently looking at starting one of these so that we can better serve our students. If the school districts can see these as a positive why can't the rest of us.
I am not sure how well I answered your question but I hope that if you have any more you feel free to ask. Further more I would maybe suggest taking some time out of your schedule to maybe look into these types of schools in your area and maybe volunteer there. I bet it would be very rewarding or at least educational as to what may be going on in those schools.
Here is a good link to a report on Alternative Education in America:
http://www.urban.org/UploadedPDF/411283_alternative_education.pdf