The biggest draw for me in this game is the combat: the ability to use my collection to actually do something instead of staring at a few rows of stars and blue/purple borders. Galactic War is a great way to play around different team comps (without suffering any competitive loss from having a less-than-stellar team defending in arena). Extending GW, even if rewards were completely removed, would provide some means of constant interaction with the game. Because I agree, after the 20-30 minutes it takes to do all dailies other than arena, I'm left with nothing to do but stare at timers and go to the forum, discord, and slack to scrounge for discussions to join. I even created an alt account simply so I could have more stuff to do with the game each day (without paying money).
If there were additional nodes (preferably unlimited) after the first 12 that didn't have any rewards but stayed at the same difficulty as nodes 10-12, there would be an opportunity to go in and test new teams, try out new ideas, or just have fun using your characters that you've spent time (and possibly money) gearing/starring. You could even have achievements or some other means of tracking a player's personal best record on GW run duration to give some kind of goal. Keep the same mechanics of carrying everything over, so people are still stuck with their roster like normal GW, but I think it would give a lot more freedom to play around with characters and interact with the game. Best of all, it wouldn't really cost CG any revenue - no rewards or benefit other than satisfaction with the game, so presumably there would be no reduction in crystal sales.
It's my understanding tournaments were added in response to a general interest for more combat/activity in the game. This would be one means of satisfying that desire to do more with a player's collection that wouldn't affect new character releases or have any negative impact (because people can choose to do it or not, and there are no rewards so if someone can't beat node 12 they're not missing out on anything), at least none that I can see.