At some point in the future marketers will learn about AGI, and we'll have to make yet another term, maybe artificial general practical intelligence?
There is nothing on the word "intelligence" to imply it's not specialized.
I know what agi is; I just find the terms backward.
It's perfectly ok to prefer the qualifier to go the other way around, keep intelligence general and change the name of the specialized form. But that's just not how our language evolved.