Correct. Would you let someone that didn't go to medical school perform surgery on a loved one?

No, but I'd be okay with them writing software for me if they had shown an aptitude to do so. What an incredibly weird tangent to go on.

Some people would be fine with it. But enough people do care that we have separate terms for "doctor" and "medical enthusiast". It's simply your priorities and those of society at large that determine the importance of the distinction.

Doctors don't just "go to medical school". They are licensed professionals who are required to complete extensive theoretical, practical, and professional education in a system designed and governed by the state and relevant professional bodies. They take an oath, and they are personally responsible for their mistakes and the consequences of those mistakes. They are required to conform to a rigorous system of ethics, and they can lose their license and their livelihood if they do not.

All of these facts are also true of "real engineers", and it's why coders are not "real engineers", regardless of whether they have a CS degree.

Not sure how putting my point aside to enumerate some unrelated facts about doctors supports your position. I'm just explaining why we have different words for "engineer" and "coder", it's fine if the distinction isn't useful for you.