Physicists seem to be doing a pretty good job, mathematicians as well.

For some areas of physics. In my field(plasma physics modelling), non-open source codes abound.

Why? Who owns them?

There are some understandable reasons, some of them related to them containing potentially export controlled models. Even then, you could strip out those bits but for some reason, no one does it because they see no need to once they have access to the code. Often a hefty (for academics) license of 4 figures a year gives them access to modify the source code but they can't share their modifications with others.