But putting aside standardized tests, in the context of this discussion about Stanford, I think these accommodations are being used for ordinary tests given for classes, so Stanford (or any other school) has full control to do whatever they want.
In real life, you're rarely given unlimited time for your tasks, and workers who can do more in less time are considered better than the ones who always need deadine extensions, so why not grade that too?
I'm also fine if a teacher or organization decides they just want to evaluate competency at the underlying material, in which case I think a very generous time limit should be given. Here the time limit is not meant to constrain the test taker, but is just an logistical artifact that eventually teachers and students need to go home. The test should be designed so that any competent taker can complete well in advance of the time limit.
I only object to conditionally caring about the thinking speed of students.
It's that much harder to change the rules of standardized testing for all students, for complex and possibly dubious reasons, than it is to make an exception for small number of clearly disadvantaged students. One is inviting nation-wide political discussion on the merits and fairness and consequences of the changes, the other is an isolated act of charity with (initially) no impact on the larger educational system.