Mechanical engineering. Electrical engineering. Civil engineering. Chemical Engineering.Some of the least intelligent people I've met were highly educated, and like vegans spared no moment telling you about it.
What kind of engineering? I'll use (one part of) my field, where the "software engineer" title I personally feel is thrown around like Oprah audience prizes. "You're an engineer, she's an engineer, he's an engineer, you're all engineers!" Some are well educated with CS degrees. Some are actually brilliant and had no formal education at all.
I get your point on doctors and dentists, but the crux of your argument most certainly cannot be applied universally.
I am not talking about titles (everyone in a bank is at least a VP, including tellers). I am talking about function.
You don't want a HS grad designing the bridge you drive over. Nor the skyscraper in downtown.