In my experience so far in the BME field, there are more cons than pros. One of the cons is what you mentioned above, BME is too broad. In the company I worked for, a lot of the engineers studied Mechanical Engineering. Most of them said they decided to obtain a more specific degree while taking BME courses on the side. This allowed them to be more marketable to employers. I was involved in the interview process of searching for interns. I noticed that for our manufacturing intern position, we leaned more towards students who majored in manufacturing over BME. I do believe BME is a great field, but I feel like it takes a little more work than other engineering fields.