I'm sure it is a licensing issue. If they had agreements for the models or the sound files they'd have to pay those people. I think doom was released without the original sound files. Perhaps that was quake.
It was not a licensing issue that prevented id game assets from being released. Carmack wanted to share the technology, the knowledge, so others could learn from it and improve on it. Letting people play doom/quake for free was not the purpose at all.
I very much doubt that. Generally, either the publisher or (sometimes) the developer owns it all. In the case of EA, those entities are the same. I can't see EA open-sourcing anything, ever, though.