The main issue is that AE graduates may have more difficulty getting non-AE jobs, while non-AE engineering graduates (e.g. ME) are competitive for AE jobs. I.e. having an AE degree may be more limiting in terms of seeking jobs outside the specialty, but does not confer a similar advantage over others within the specialty – and being tied to a specialty may make job prospects much more dependent on that industry’s business cycles.
ME with AE electives may be a way of doing “AE” without giving too much of a limiting signal to employers.