To encap....in most states, anything deemed to be engineering work (plans, specifications, evaluations, reports, opinions, etc.) requires that it be done by a licensed professional engineer and so designated by signing and sealing. It does not have to be a "public" project. Specifically, in the state of my primary practice, if you are an employee of a corporation providing engineering services, ALL technical documents as engineering works submitted are to be signed and sealed by a licensed professional engineer, without regard to their application on public or private projects.
I'm not aware of any building department (unless you're perhaps the building official's cousin in Podunk) that will accept plans for a structure that are not signed and sealed by an architect or engineer, and architects are limited as to the scope of their responsible works, so engineers are typically responsible for signing and sealing certain segments of a project such as structural, mechanical, civil, and electrical.
No, those of us who are licensed professional engineers are not elitist. We are ethically and legally charged with the protection of the health, safety, and welfare of the public in our respective areas of practice. The "public" does not only mean "public projects". Yes, we get a bit testy when unlicensed engineers hold themselves out as equivalent in the public realm. They are not. If they design something and it goes awry, the only recourse the "public" has is to sue them in civil court for damages. If a licensed individual makes a similar mistake, the individual is then statutorily and civilly responsible, with the risk of a loss of license to practice. Each time we sign and seal something, we put a hell of a lot more on the line than an unlicensed individual.
Try getting professional liability insurance for performing engineering services without a license. I doubt it's possible.