I think the world has changed. In earlier times one man, often a celebrity chief engineer, head designer call him what you may, could wield a lot of power and make huge calls often with stunning results. Sometimes sadly with startling failures and loss of life too. In these more litigious days, insurance companies call the shots and no one person wants or is allowed to carry the sole responsibility. Engineers are degree qualified, members of professional institutions and major design decisions are mostly made by committee.
A lot depends on the field of work but in my experience working for 35 years in the automotive manufacturing and R&D arenas the best engineers were always the guys who had a thorough grounding in the basics, often completing an apprenticeship and qualifying as tradesmen before going to Uni and doing a degree. Indeed in Germany and Japan this is the norm rather than the exception. These people understand the intricacies and issues involved in manufacturing, how different materials behave, not just their physical properties but how they are machined or moulded and what affect their choices could have on the process. Fitters and toolmakers have a lot more respect for their engineer if they know he could set up and run the machine himself if he had to.
Since the auto industry died here in Australia, I've gone back to my roots as a tool maker and I work at the uni as a prototype machinist / fabricator designing and making trial parts, spares, test rigs etc supporting a number of different research groups. Work which involves use of all the standard workshop machinery, Lathes, mills, surface grinder, sheet metal press brake, Tig / Mig welding stainless and Aluminium etc. it is wonderful and I have not had so much fun at work for many years! I have rediscovered the joy of getting my hands on the tools and realised how far away from what originally drew me into the industry I had gone in my previous engineering roles, sat in front of a CAD screen or an Excel spreadsheet for hours on end. I only look at computers now when I want to and its great!
