Special Accomodations and Proving Disability

It seems to me that a lot of disability accomodations go about it the wrong way. They have a certain thing everyone is supposed to do a certain way. When a disabled person says 'This is not fair. I can't do it that way' (or they can't do it as well as expected) then the system says 'OK, prove to us you are disabled, and we'll put you in a special category that get to do it a different way.'
There are several problems with this model:
a) it depends on labels and testing for disability. If you're undiagnosed or misdiagnosed, you won't get the help you need, even if you know that you need that kind of help. Even with an accurate diagnosis, you might not quite meet their criteria and still not get any help. (For example, some autistic assistive communication users have lost needed services because they now score over 70 on an IQ test.)
b) just because it's not as desperate for normal people as it is for you doesn't mean it wouldn't be helpful to them. Very often, disabled people can signal a problem that affects many people, simply because it affects them more. But if you single them out for help, the others with less acute needs for the same thing don't get it. For example, one study tested the use of voice recognition software to create 'subtitles' on an overhead as a professor spoke. This was intended for several deaf students as an adjuct to signed translation, but several hearing students also started looking at the display. Some people, like my mother, find it easier to understand text than speech, even though they aren't labeled with any disability.
c) it singles out the disabled person as a 'special case' rather than treating them as part of the group. Because there is no accomodation for differences except in extreme cases, other students may come to resent the disabled student for getting special bonuses (I remember how upset I got when the teachers let my CP classmate chew gum in class but wouldn't let me do it) or else pity them for needing those accomodations. Granted, there are many reasons for normal people to have negative views of disabled people, and changing this one thing won't eliminate that completely. But it will help.
What is the alternative? Make accomodations available for everyone, like they do with curb cuts, elevators and talking walk-lights ("the walk-light to cross college drive is now on. Bee-dup."). It won't really lower the quality of performance in a class if kids are allowed to type essays rather than writing them longhand (of course, they should all be getting practice writing longhand, too) or a professor passes out notes to their lecture to any student who wants them. In cases where there truly is a different need, such as teaching different subjects to a developmentally delayed kid than to their classmates, there are two options - either let people self-select which system to go with, or accomodate everyone regardless of labels (with this specific example, a system where children work on units and go to the next one as soon as they pass the earlier one would work well).
If we do it this way, undiagnosed disabled people will still get the help they need, disabled people won't be singled out as 'special needs', nondisabled people who'd benefit from certain accomodations (such as gifted kids) may be able to get them, and the time-consuming, wasteful and adversarial beaurocracy of determining who gets help will be eliminated. Even if we don't do this for every accomodation, we can do it for most of them and get similar benefits.