I never really go the appeal of unlimited time on tests, unless you actually have a diagnosis that requires it. I saw it around me when I was in university but I am unconvinced that it actually helped any 'normal' student.
I mean, what are you going to do with unlimited time anyway? Sure, some tests are designed to be too long for the allotted time, but most aren't. If you need more time on a test that is designed for the normal amount of time, what is going on? Are you deriving formulas that you neglected to memorize? Possible I suppose, but how many students are clever enough to do that correctly on a test when needed but don't just know the material in the first place?
Extra test time as an unfair advantage makes even less sense to me in subjects other than mathematics and physics. What are you going to do, derive an answer to "Who were Dizzy Gillespie's primary influences?"?
If it wasn't mathematics or physics, I was always fucked if I didn't know the answer within half a minute or so of reading the question. Even with mathematics or physics, if I was spending much time at all deriving things, it was generally a sure sign that I had failed to prepare and was fucked regardless.
Here is my hypothesis: Much of the elevated diagnosis rates at upper-class schools reflects the fact that people with more money are more likely to acquire diagnosis for non-life threatening ailments their children have. The rest of the elevated diagnosis rates is probably just rich people throwing money at the wall and seeing what sticks. I doubt it gives them an advantage, but they have the money so it can't hurt to try.