Take wind as a paradigm for emergence. (1) Something heats the ground, (2) making the air expand and drop in pressure, (3) making an air flow from higher to lower densities.
But the “something” at stage (1) can be the sun on a lake or the firestorm wind made by a bomber squadron, and so the paradigm for emergence is indifferent whether a natural or intentional process leads to an emergent property.
So what would it mean for the intentional as such emerge? We can’t use a paradigm that allows for both intentional and non-intentional initiation and then say the intentional needs to arise emergently. Said another way, it can’t be the nature of the intentional to arise emergently. But isn’t the whole point of describing the intentional (or consciousness) as emergent to give an account of the sort of thing it is?