The idea is ownership and rights. Nintendo owns Pokemon. Nintendo does not own Golden Sun. Or at least, not enough of it. Nintendo just publishes it. However, I did some research on the matter. Every source I came up with for Pokemon said Nintendo wholly owns the series. With Golden Sun, it's a little tricky. Nintendo has ownership as they publish it, however, Camelot is the developer. I'm not sure how all the inner workings work, but Camelot would have a lot more say in the matter. The two companies are second party in relation to Nintendo, however, the deal are much different. Camelot is likely in a contract with Nintendo. If their relationship expires (either by the end of the contract or Camelot just leaves) Camelot walks away. If Gsme Freak leave, Nintendo still owns most of Pokemon and can buy out the rest. Because they own 66%, they can have someone else make the games. There is a huge functional difference.
The reason I say this is not because it seems cool. It's a pattern. Nintendo added in many first party titles over second party titles.
You're right, Nintendo probably does own more of Pokemon than it does Golden Sun, or other 2nd party IPs. However, so far there is not specific evidence that Sakurai will exclude them on that basis. Just because they haven't been included yet, (other than Pokemon) doesn't mean the pattern you've interpreted is an actual rule Sakurai adheres by. The series added so far have out-prioritized the series not added, whether they be first or second party. It's not like there was a character from an unrepresented series more deserving to get in than the series added.
Now, I'm not denying that it would be harder to include 2nd-parties, but Sakurai has also previously shown with both Pokemon and 3rd-parties, that he is willing to make the effort needed to procure a character he believes it is warranted, and the character merits inclusion. As he previously stated, at the time of Brawl he didn't believe any other series (other than the ones he mentioned) warranted inclusion. The fact is Sakurai has already gone through legal negotiations with Camelot, Treasure, TOSE, and Noise (among others) to have their characters included in Smash in some regard, he could very possibly do it again. There has been no proof so far that Sakurai is unwilling to include characters not wholly owned by Nintendo. He even included characters not even partially owned by Nintendo. Smash's roster isn't, nor ever was, solely dedicated to first-party games.
If you're trying to say that (for example) if Camelot split from Nintendo, for whatever reason, Isaac and GS would be yanked from future Smashs, then you're probably right. Chances are Camelot would retain the GS IP while the battle for Pokemon would be epic and bloody but would most likely result in Nintendo keeping the IP. If Sakurai didn't want to include characters that didn't have safe, sure futures in Smash, he wouldn't have included third-parties. Nintendo has no part in the decisions of Sega, Konami, or any possible third-party company in Smash, yet Sakurai made the effort necessary to include a character for, as far as he knew, only one specific game in the series. The third parties could choose to abandon Nintendo's platforms forever if they so desired, yet their characters were included among first-parties. Plus third-parties would have even more say over their characters than second-parties, yet Sakurai accommodated all their wishes.
If the third-party barrier has been broken, it should pretty much show that legal ownership and creative control don't effect Sakurai's decisions much if he believes the character merits inclusion. And if he thinks third-parties do, there is really no reason why he wouldn't think second-parties could. Like I said, the reason more second-party series haven't been playable yet is because they haven't been as big, as prominent, or as important as the series included previously, not because Nintendo isn't the sole owner.
Golden Sun was just as big as Pikmin. The Golden Sun games outsold Pikmin by a hair and were very popular games. As Chrono mentioned, it's a reason we got a third game. There were also only 4 Nintendo series in Brawl, so Golden Sun would have not been out of the question. However, the only thing from the games was an assist trophy and a song. Pikmin got a lot more for being a series that was far and beyond comparable to Golden Sun.
Golden Sun might've been just as big as Pikmin in NA, but in Japan and in general it was not. I'm not denying Golden Sun was popular, and that was why we got a third game, but in relation to Pikmin it just fell short. Pikmin outsold GS by roughly 100k, and in Japan (where popularity matters far more, especially back in Melee and Brawl times) the Pikmin sequel sold almost double the Golden Sun sequel (The Lost Age). Plus the fact that Olimar was in general more popular and more requested than Isaac (again, especially in Japan), and the fact that notable series created by Miyamoto do seem to be treated specially. Now Isaac could've hypothetically been next on deck, new-series-wise, but his series, while popular, and critically adored at that point, was still not as big as Pikmin.
There were six new playable series added to Brawl, and those with enough to really work with (all but ROB) received a stage, trophies, stickers, and music, as well as many other distinctions in the game, where the roster was divided up by series. Sure there could've been more series added, but adding a new playable series is a lot more work content-wise than adding another rep from an existing series (and is most likely why the entire Forbidden 7 - plus perhaps TL, Jiggs, and Wolf - were from already existing series). It was still double the amount of new series Melee got.
Pikmin got a lot of content because it was the standard of playable series to receive a stage, trophies, stickers, and music. Any other series that was hypothetically made playable would've also received all these - other than perhaps a series with very very little to work with.
The truth is in the results. Nintendo owns all the series that got in. Pokemon is still controlled by Nintendo and most sources say that it is owned by Nintendo (see below). The reason Sakurai ignoring these series on the DOJO is important is because during that time there were tons of second party series coming out. All of them were added as assist trophies, not characters. Golden Sun is an important case because it was bigger than Nintendo's own first party series. That same series got more music, a stage and a whole character. When I mentioned the trophies for Magical Starsign, I mean they get more of a focus. I'm waiting for my theory to be proven wrong, though I doubt it will. If you don't see a second party character in the next one, then I'd say it's true.
Yeah, again, Nintendo owns the majority of Pokemon, not all of it. They don't have complete creative control, they don't even seem to have control of what/how it's implemented in Smash. To include Pokemon, there still needs to be legal negotiations with both Nintendo and Game Freak, like the procedure would be for other 2nd-parties. Other than that (and the third parties), yes, Nintendo does have complete control of all the series so far included in Smash, though, and I hate to sound like a broken record, with the exception of retro series, they have all been bigger than any other 2nd-party series. Golden Sun and Pikmin were close, but GS was never bigger than any already-included series, at the times of inclusion. I still don't see what the Magical Starsign trophies have to do with anything, they didn't get any more trophies than some 2nd party IPs.
All in all, who knows, there is a chance you could be right, but as there has been no precedent yet in which a 2nd party IP
clearly is omitted for lesser 1st-parties, right now, as you admit, it is just a theory based of an interpreted pattern, with no proof as of yet. Again, all I'm saying is that we don't know yet, the situation in question hasn't arisen yet, but when/if a 2nd party gets passed up that was without a doubt larger than other series added (at the time of inclusion), I will concede. Before that, we shouldn't assume things that haven't been proven.
You can respond if you want, but it pretty much comes down to wait-and-see, so I don't have much more to add.