There even is one interesting dialogue choice that points out how broken "one illithid persuation per day" actualy is:
When you approach Spike, with Wyll in your party ... you have option to connect your mind with Wyll, wich consumes your Illithid dialogue charge per Long Rest ...
What is funny tho, is that inside that dialogue choice, you have ANOTHER [illithid] dialogue choice ... wich you can never use, since you used your charge to connect your mind with Wyll ...
And if you decide to not connect your mind with Wyll, you never get to this hidden choice.
I keep wondering from the beggining of EA what can be hidden there ... and how are you suppose to get it.

As far as I can tell from parsing dialog options, whenever you see this message...
*You focus on the source of the power, but it is quiet and still. It needs to rest.*...there's no other consequence to the Illithid dialog option that led there. Said another way, you will
always fail the check. 😭 I'm more concerned with the Illithid dialog checks that you can pass or fail.