Engineering shares some characteristics with the medical profession. There can be huge consequences to every decision. Physicians intern to acquire the practical experiencve to make these decisions 'righter' more often. Engineering is similar. You can know all the math, but how to apply it appropriately is the art in engineering. Most engineers are considered junior for at least the first 5 years.
You're right but Engineering (with the exception of certain corners, ex: building bridges) isn't quite as cut & dried as medicine. It gets downright blurry in some areas. You can invent/design (Engineer) a widget, manufacture it in your garage, and sell it locally or on eBay. There is no law saying your widget must be designed by a Professional Engineer or even reviewed and stamped by one. But there definitely laws saying that you can't perform sex change operations in your garage.
I am in a position that, by my own admission, I should probably be prohibited from occupying. My title at work is Controls Engineer but I have no Engineering degree (or any degree, or any kind of certification whatsoever) yet I am allowed to design systems to control machinery that has the potential to kill people in gruesome ways if I don't do my job right. How is this allowed to be true? I honestly don't know. I know the law (in TX, and I assume similar elsewhere) says that my employer can give me the title of Engineer as long as they don't introduce me to clients as an Engineer for hire. I am allowed to design equipment used in-house and would be allowed to design consumer products for sale, if that was the kind of business my employer engaged in. But for my own business, I can't use the word "Engineer" in any of its forms.
Imagine what the Engineering departments look like at factories that make dildos, bongs, fidget spinners, hammers, etc.; do you think they are brimming with pedigreed folk? I doubt it. Somehow what I do is no different (although personally I think it should be).
There is no medical equivalent to my position. Closest thing in the civilian sector is probably a nurse practitioner but actually probably more analogous to a combat medic. I have the authority to do just about everything a doctor would, except for certain niche situations that don't come up, and without the long academic requirements. I have been doing it so long that, had I actually gotten my degree, I don't think I would remember much from school and I would have 4 years less experience.