Opinions on this are very conflicted, as can be clearly seen in the Licensing thread
Well, if there’s no reference to any source code or open source license, it’s probably closed source 
How would you enforce this? Even if you required posting some form of source code, the related programs would have no way of checking whether that’s actually the full source code of your program. You could just attach Hello World and nodes would have no way of telling. If you want to rely on people’s votes instead, you open up the possibility for censorship even of open source apps.
The reason these networks are independent is that they’re just different from Bitcoin enough as to be incompatible. Even Bitcoin’s own testing networks.
Which is why I can’t agree with your opening proposition. I like the idea of an open-source world, but I like the idea of a distributed, uncensorable P2P network more, and I care more about the success of that than having everything on it be open source.