We don't have patents or copyright for math. It is not that we want mathematicians to not get paid, or that we don't value math, or that there is no room for both paid and free math. It is that math is such a fundamental building stone that allowing rent seeking in that space would cause significant harm to society, including the advancement of science.

Some software is like a book. You buy it and consume it. You don't buy a book and build a better book. You do have the problem with schools in that children would be harmed if they had to pay for it, so we have libraries and school that buy the books for them so they become "free" for the children. Some nations, like Sweden, also have laws that demands that book publishers send books to libraries and the money the copyright owner is set by the state.

If we treat software as math then it should be free. If we treat software as books it should be semi-free for those that needs it and can't afford it.