There is no such thing as IQ either its also a conceptual model. But agree there is no such thing as EQ.
The argument seems to be that there is no such thing as EQ because it is not a workable conceptual model whereas there is a thing like IQ because it is a workable conceptual model - definition of workable conceptual model that it can be used to make good predictions as one generally likes to do with conceptual models.
It's a concept which we use to describe certain abilities in humans but there is no IQ sitting somewhere. While EQ is definitely close to be "fraudulent" it's still sitting on a gradient with EQ being the best model we have when externally accessing someones mental abilities but it's not a thing, it's a human construct.