That it is a widespread misconception is exactly true. That it is was the constitutional Delegates intention to use this standard as the basis for American citizenship is contradicted by quite a lot of evidence, Madison's commentary on State citizenship not withstanding.
I don't think the Founders would be too happy with birth tourism, but I also don't think they saw it coming. And I know they didn't put anything in the Constitution to prevent it.
The problem with this issue is that so many people "KNOW" things which aren't true. Your perspective is simply the product of endless repetition by lawyers for the last century and a half. Documentation which comes from the Founding period indicates this modern notion is incorrect, and that citizenship was not simply a matter of being born on a specific side of a border.
When Madison and others are referring to being "born here", they are not referring to just physical borders, but borders which establish someone as a member of a community. They excluded Indians, and they excluded slaves, they also excluded the children of British Loyalists. The problem with modern interpretation is that they are looking at things too simplistically.
I would be in favor of changing the Constitution to shut down this industry, but that's what it will take.
There is no need to change it. There is only a need to stop interpreting it incorrectly.