You just describe ONE way. MIT License isn't giving up Open Source, as all Open Source projects with MIT prove it. Also the world is not only about GPL, there are other licenses in effect that either cannot or don't want to change. In that case a program with MIT could be used and helpful for the project. In such a case its better to have a MIT licensed Open Source library instead a proprietary library, even if the whole thing is not GPL licensed (whatever it ends up being). Not all Open Source licenses are compatible with GPL, or even proprietary licenses. So having the coreutils as MIT licensed software alongside its original GNU GPL versions are not a bad thing. It's only a bad thing, if you want to enforce GPL code for any derivative works.

And not every project or maintainer cares if someone contributes back. In fact there are a few Open Source projects (even licensed in GPL) that does not operate on a community basis and do not accept code from others, other than a closed circle of chosen developers. Also MIT license is much easier to understand and grasp and does not require a lawyer to understand it (I read it multiple times and there are still bits I get confused or forget over time). It is also less risky for companies (or for any individual for that matter, who is not well versed in licensing and just want to license a simple program in example). Meaning if a company is afraid of using GPL and they make a mistake, everything needs to be Open Source or they could get sued. They could decide not to do partial Open Source. In that case a partial Open Source with MIT License is the better choice.