I'm not sure about that. In my department we've had full-ride fellowships go unfilled for lack of qualified U.S. students to fill them. They shy away from this particular field of engineering because they don't see a future in pursuing it.
So funding is one aspect of a multi-sided coin. Having qualified students who are interested in the discipline.
Well, if there's really not much future, the students could be right in staying away. Which branch of engineering are you referring to?