Personaly i think this is missconception.
Illithids are not emotionless ... or at least i never find any note that they are ... like for example Lizardfolk, wich have that written in their most basic description.
Their mind works differently from ours, but that is all we know ... or at least all i know.
Personaly i would say its just that they have no way to express them ...
Their speech seem emotionless, bcs they are not talking ... they are projecting raw information right into your brain, that interprets it as inner voice ...
But that is the problem, that information is just not complete ... like when AI reads a text, it says all words corectly (sometimes xD), but it cannot provide any tone or emotion else since those data are simply not there.