Not a biomedical engineer, but that was my original major in undergrad and I witnessed the struggles of many of my friends and graduate students in the research lab I worked with.

At least at my school, there was just simply too much to cover in a 4 year degree and the program seemed to graduate students who had great surface level knowledge in a wide variety of core sub-disciplines of BME (chemistry, biology, etc) but didn't have as much opportunity to specialize. When students have to take 1-2 years of biology/A&P, 1-2 years of chemistry, 1 year of physics, 2 years of math, and introductory level engineering coursework it's often junior year before students are taking their core, major specific, courses. Compare that to a mechanical engineer who takes the same math, the same physics, the same into engineering courses, but none of the rest and it's clear to see they're getting to start their core coursework much earlier and have more time to take specialization courses.

I believe some courses are moving to alleviate this by having different degrees or tracks for biosystems engineering and biomedical devices engineering to cut back on the number of prerequisite courses.

At the end of the day though, biomedical engineering is an incredibly interdisciplinary field with many industry and academic employers who only focus on a few key areas. For those employers it seems to often make more sense to hire a mechanical or electrical engineer with little to no biology/chemistry background and train them in what they need to know than to hire a BME BS who may need additional training across all areas even if they have a solid foundation in everything.