I didn't mean to start a controversy, but here goes.
I have a MSEE and worked 45 years as a consulting engineer, employed by G.E., ABB, and several small "engineering" firms. I designed and implemented training simulators, real time control software for nuclear power plants, and the industry standard software to analyze power systems, and real time software that controls parts of the USA bulk power grid. Yet, I never got a Professional Engineer's license.
At the organizations I worked at, only 5% or so of the engineers employed had a P.E. license. What is true is that the organization must have at least one P.E. employed, and certain projects require the P.E. signature. The article cited by Travis King says:
Engineer title restrictions are most strict in situations where someone is attempting to offer consumers consulting or contract services. They are also strict in situations where engineering is practiced in the public sector.
That leaves non-public non-consumer fields as mostly non-restricted. Those happen to be the lion's share of commerce needing engineering.
When Boeing hires 30,000 engineers to work on the design of a new plane, only handful of them are required to have a P.E license. A utility hires a consulting company to design their transmission grid (i.e. a design study.) The consulting company is not signing off on the design (the utility's P.E. does that) nor are they offering any services to the public. In both cases, the actual work is done by an army of unlicensed engineers.
The original question in this thread was whether there is room for someone without a degree. Clearly yes.
Perhaps someone else can find the actual number of licensed professional engineers compared to the number of practicing engineers with engineering degrees. My guess is 5%. The NSPE (professional engineers) has 35,000 members while IEEE has 400,000, ASME has 130,000, ...