" There is not a single person that can claim to perform both tasks."
My first degree was in mechanical engineering, after which I spent about 10 years working in various engineering roles in metal processing, cable manufacture, aerospace components, electronic packaging and food processing.
In my early 30s I left work to spend two years working for an MA on an industrial design course aimed at converting engineers into hybrids. Hard work it was, too.
Six or so years on from that I am working as a freelance designer AND engineer. Some of my work is filling in specific gaps in teams, some of it starts with a clean sheet of paper and a client brief. In this instance, concepts are mine, ergonomics / usability are defined by me and I get involved with field testing, visuals are mine, test rigs are mine, project management is mine, engineering is generally mine, development and testing is mine, production CAD is most definitely mine to the point where it goes to the fab shops. Heck, I even dabble in electrical system work and PLC programming for rigs.
I'll admit my sketching can be ropey, tho it is sufficient to get ideas across, and that I do call in experts when I get out of my depth (electronic system design, complex analysis problems, CFD etc).
Sleep deprivation comes with the territory.
I am based in the UK. There are a couple of schools producing talented designer / engineer types, some of whom are extremely (multi) talented. Some of those that have been through the system have names that you might recognise and whose products or work you will have used or benefitted from. I have been working for a bit with another independant who made the transition at a younger age than me and a fair proportion of his work has made it into the shops.
Beware sweeping statements.