BME tends to be too broad of a major to give you any real depth in a single area. It tries to incorporate some biology and some engineering and ends up being a little bit of everything and not enough of one thing. HCI (human computer interaction), prosthetics, robotics, and mechatronics require considerable knowledge of mechanics and dynamics, electronics, and controls. A BME major does not delve far enough into any of these areas to be useful, at least not at the undergraduate level. Most jobs in the biomedical engineering sector tend to go to those with degrees in traditional disciplines like ME, EE, ChemE, etc.
With BME, you would have to get a graduate degree at the least to develop a strong foundation in these areas. That doesn’t mean an ME, EE, or CSE major wouldn’t benefit from a graduate degree, but a BME would need a graduate degree.