Here is the dirty little secret of the ADA.
I worked for the State of California when the ADA was passed. The edict came down from back channels: you will NOT hire anyone with a disability unless through special self-funded programs. "Regular jobs" will NOT be filled by the disabled.
Why? Because the ADA makes it IMPOSSIBLE to terminate an employee with disabilities. By then we were able to terminate EEO hires WITH CAUSE (and a lot of hassle). But if you hired a disabled person and they NEVER showed up for a single day of work, you could not terminate them without a HUGE hassle, and even then it might be overturned.
It is easier to fend of accusations of bias before a legal relationship is established. Afterwords, not so much. And there is no such thing as "equal job qualifications." There are enough soft variables to choose one candidate over the other as long as they have similar degrees, years of experience, etc.
And the ADA has become such a monster, I must assume those conditions are still in place.
The Laws of Unintended Consequences: There is a reason why it is a Law.