Test folks have totally different systems like LabView for data logging and analysis that don't really talk to the simulation tools, CAD, etc. - very fragmented dev tools.
I really like Bret Victor's "Seeing Spaces" vision for a more integrated hardware dev environment where it integrated software and workshop into an real-world "dev environment": http://worrydream.com/SeeingSpaces/
I believe it actually takes a bigger and more hierarchical engineering organization to have MechE's who are not busy at the CAD terminal a lot of the time.
In addition, our machinist has a CAD seat, the machine shops that we use all have CAD seats. And while optical engineering is a small field, most OE's have CAD skills.
Machinists running any sort of CNC machine will need both CAD & CAM seats.
[1] https://www.youtube.com/watch?v=yPtoxEgzrhE [2] https://www.youtube.com/watch?v=3-jT3HrSHjE
Unless you're an EI fresh out of college, engineers probably won't spend many billable hours in CAD. Your time is too valuable, and most contract rates won't be high enough to have engineers doing drafting.
(EI = Engineer Intern, for getting your 4 years of experience for becoming a PE, which is similar to a Medical Resident for physicians.)
We have a pool of draftsman that handle most of the actual drafting, at the direction of PEs, which let's the PEs focus on actual design and other things that can be billed at higher rates.
But since CAD is still installed on the PE's computers, they're probably still counted as users, even if it's mostly for review, printing, minor redlines, etc.