I think the OP has some very good points, but I would argue that the problem is not exclusively that you can only get war goals for a handful of planets. The problem is that you don't get enough warscore for taking your war goals, and you have to pretty much conquer an entire 12 planet empire to take those 3 worlds you declared for. This is both counter-intuitive, and counter to how some of pdx's own other games, like CK 2, work.
In CK 2, if you go to war over a county, then although you can get points toward warscore in other ways, the #1 way of earning points comes from who controls the contested county (or duchy). If I fabricate a claim on Padua and attack other counties, my enemy will gain a ticking warscore in his favor because I have not taken the wargoal. Conversely, if I conquer Padua early and hold it, even though the enemy is sieging other land of mine, I'm still gaining warscore for holding Padua.
Stellaris could, and should, work the same way. If I declare a war for Earth, Proxima Centauri, and Alpha Centauri, I should *have* to take those worlds, specifically, to most efficiently get warscore. If I take all 3, I should get pretty close, say 75% warscore. Then if I hold them, I should get +X% per month (I suggest 1-3%, they will have to playtest). I have conquered the worlds, and held them... I win the war. I shouldn't have to take the whole rest of the Vulcan Alliance out once I have those 3 worlds.
The way it is now, you could declare on a federation, ask for those worlds, conquer NONE of them, at and the end of the war, still be in possession of those worlds. This is contrary to logic and also allows sloppy/bad strategy. I can declare on one guy but conquer the weaker neighbor and I could still get the stronger guy's worlds. In what universe would that happen? It's counter-intuitive and unrealistic.
If they did just this -- made taking and holding all war goal planets for a certain period of time get you to 100% warscore and victory, I think a huge number of other problems would be solved. No it would not fix that you have to war someone down 5 times to finally take them. However, at least when warring them down, you don't have to conquer the same freaking 12 worlds over, and over, and over again just to get the 3 you want. I think THAT is part of what leads to the fatigue. If you are more powerful, and you win, you should only ever have to conquer a world once. That by the end I have conquered and occupied the same several worlds 5 or more times is where a lot of the feeling of tedium comes in.
Heck, I play co-op, and last game, my friend and I were joking that my soldiers had been to this one world so many times, they have time-shares on the planet and concubines and such, heck maybe even families by now. I mean... come on. It should not be like that.