The reality is biomedical engineering is very much a niche atm.
I would possibly call it an application rather then its own type of engineering even though there are now BME degrees.
Id bet most engineers in the field would probably come from a field like applied physics, mechanical, manufacturing or materials engineering/science. For example if you work on designing artificial tissue this is probably a materials expert understanding the properties of skin, developing next generation MRI machines are probably physicists, and developing new techniques to 3D print implants would be a manufacturing engineers…
It’s very hard to compare it to conventional engineering degrees as it has a very small footprint and is really pulling different bits from traditional disciplines. Id certainly say employability wise you are more pigeon holed there however, with all engineers you generally can move to other industries if you want to (and most importantly demonstrate value to employers, far more of a graduate success comes from there competency as an engineer and ability to communicate this rather then the specific domain of there undergraduate degree).