I don't doubt that if it were very obvious that you were interacting with an AI, many people may be put off by it.
On the other hand, isn't an adaptive exam like the SAT also an instance of you having to work with some automated system to somehow "prove" yourself to that system?
I'd even argue that what I am proposing (I wrote the linked piece in case it wasn't obvious) ultimately leads to someone reading the chat transcript to gauge candidate suitability. That should reduce the stigma of having to abase yourself to an AI, no?