The hierarchy could be inverted with a very small change to the laws governing engineers, just as it has been done for lawyers. The details vary by jurisdiction, but generally lawyers must practice in some form of partnership where non-lawyer members are restricted. Work similar to project management is frequently performed by secretaries that are subordinate to the lawyers.
Whether or not strengthening the profession of engineering would be good for society is another question. It is inherently anti-competitive. It could easily slip into a system with very few and highly paid "qualified" engineers whose small number would hinder development. This is a problem with medicine and the supply of doctors in some places.
I would note that in the legal field, effective DOJ threats have prevented any attempt to limit the supply of JD grads, while the other rules such as management of lawyers by non-lawyers has remained in place.
Whether or not strengthening the profession of engineering would be good for society is another question. It is inherently anti-competitive. It could easily slip into a system with very few and highly paid "qualified" engineers whose small number would hinder development. This is a problem with medicine and the supply of doctors in some places.