If you are writing a library, the moment you include GPL, you can't be Apache nor MIT nor BSD anymore. You yourself have to change the license so that your close source users are excluded (or forced to give put code). It is right there in GPL license. Only ideology is related to following copyright law. And maybe also respect toward GPL software creators who don't wish their code to be used.
You can legaly include apache in GPL software.
Following your theory, one would either have to break GPL and risk legal problems or exclude close source users of his work.
If the goal of the library is to be used in closed source, you will be limited to reusing code to only those that has compatible license with the closed source. That is a choice you make that has nothing to do with writing software to fix problems that people have in their lives. In some cases this make a economical sense, where you do not just want to solve problems for customers but where the primary goal is to generate property for which the company can own. For other companies, solving problems for customer is how they get paid and the faster they solve one problem the fast they can go to the next.
But I digress. There is a clear bright line between writing code to solve a problem, and rewriting code because the license don't let you create property in the form of closed code. One is about pragmatic problem solving, and one is about ideology. One allows for code reuse, one is limited to my-way-is-the-only-way.
If you live in an ideology that demand that everything you do must be made into property owned by the company and only secondary solves problem for a customer, you will be slower than a companies which more pragmatically focused on fixing problems for customers. Don't blame others if you are self-imposing such restrictions on yourself.
"If the goal of the library is to be used in closed source, you will be limited to reusing code to only those that has compatible license with the closed source. That is a choice you make that has nothing to do with writing software to fix problems that people have in their lives."
It absolutely does. It fixes problem of people who work on close source or otherwise something incompatible is gpl. You either dont count them as people or as problems and neither makes sense. I used open source inside closed source. So yep, if I am going to five away, I will give to the same pool. Generous people gave me something, so I am giving back.
A library that I can not use does not solve any problem. That is not pragmatic, just something with limited use. Which is fine, if you feel strongly about your work use being restricted to some people only. I don't.
The moment when your logic twists gpl into literally "the only pragmatic license" is the moment when I wonder whether you are even honest in your arguments.
You can legaly include apache in GPL software.
Following your theory, one would either have to break GPL and risk legal problems or exclude close source users of his work.