Public availability of the source is a great advantage for a program to have. Many people will usually not take a look at it otherwise, for many reasons, some ideological but some also practical. [Ideology] Without the source, and without it being under a proper licence, the software will not become part of most distributions of Linux, the BSD operating systems, etc.
If you just say that your software “is copyright by John Doe. All Rights Reserved”, then it may arguably induce an inability to study its internals (including to fix bugs or add features) without being restricted by a non-compete clause, or even that its use or re-distribution is restricted. Some software ship with extremely long, complicated (and often not entirely enforceable) End-User-Licence-Agreements (EULAs) that no-one reads or cares to understand.
As a result, many people will find a program with a licence that is not 100% Free and Open Source Software - unacceptable. To be truly useful the application also needs be GPL compatible, and naturally usable public-domain licences such as the modified BSD licence, the MIT X11 licence, or even pure Public Domain source code[public-domain], are even better for their ability to be sub-licensed and re-used. This is while licenses that allow incorporation but not sub-licensing, like the Lesser General Public License (LGPL) are somewhere in between.
While some programs on Linux have become popular despite being under non-optimal licences, many Linux distributions pride themselves that the core system consists of “100% free software”. Most software that became non-open-source, was eventually forked or got into disuse, or else suffered from a lot of bad publicity.
As a result, a high-quality software has a licence that is the most usable in the context of its common use cases. These licences are doubly-important for freely-distributed UNIX software.
[Ideology] Assuming there was ever a true ideology that was not also practical.
The way I see it, an ideology (and ethics in general) are a strategy that aims to make a person lead a better, happier life. If it isn’t, then it’s just a destructive dogma, or just plain stubbornness.
[public-domain] Using a pure-public-domain licensing terms for your software is problematic because not all countries have a concept of “public-domain”, similar to that of the United States, because many people misinterpret it, and because it is not clear whether software can be licensed under the public-domain to begin with. (And other such issues).
While quite a lot of important programs has been released under the public domain, and they are doing quite fine, they may have some problematic legal implications.
For these reasons, I now prefer the MIT X11 Licence for software that I originated instead of the “public domain”.