I am going to list the "ships" I like and tell how I would like to see them portrayed in future stories. If I am going to spend time doing this, then I might as well do it in a way that will give any author in the series some good ideas.
So here are the ones that I like:
Specialshipping: Subtly written into the narrative, so I can't hate for that reason. Both characters are pretty bland when there is nothing going on and they could definitely use some character development beyond "he likes to fight" and "she's a pacifist". It would be nice to see a chapter that realistically puts them into a relationship and furthers them both as characters. It would actually be an interesting story to see some conflict between the two, actually. Red's solution to every problem is to hit it while Yellow's solution is to talk to it, reason with it, distract it, subdue it, or, after all of the above have failed, hit it only if necessary. This gives the two more characterization, can forward a theme of finding the balance between peace and violence in conflict resolution (since the Yellow chapter did not do it very well), and it would make a relationship between the two seem more believable because the two do not always agree.
Chosenshipping: Speaking as someone who actually has a bother/sister relationship with someone who is not related to me, I can say that the brother/sister dynamic does not apply with these two (or the writer of PokeSpe is lazy and doesn't want to research what such a relationship would actually look like). I guess I like them together because they are both complex characters with believable tragedy in their pasts that they both move on from together and they are both similar enough for a relationship to exist between them yet different enough that it would not fall apart after six months.
Mangaquestshipping: The two characters are interesting, have their own issues (so they aren't dating a clone of themselves), and I like the interaction between them (for the most part). My only problem I would have is if the physical abuse between the two continued in any cannon instance. What Crystal does to Gold could be classified as physical abuse. The writers should stop writing it because it's stupid and the fans should stop enjoying it so the writers will stop writing it (and because it makes Crystal look like a total jerk).
Franticshipping: I support it because it is pretty much cannon, or at least it would if the series could freaking decide where it wants to go with these two. Yes, I'm looking at you Emerald chapter. You thought you could get away with making the cannon schizophrenic just because you did an amazing crossover event, didn't you? Well, good show mate. I actually think that that is a good idea for these two. All they do is argue, they refuse to see the other person's favorite hobby as an equally viable carrier path, and, as of the Emerald chapter, they are old enough to be freshmen in middle school (aka: sixth graders). While I do know that middle school sweet hearts do exist (if my EVAN professor is to be believed), such relationships tend to be on and off ones.
You know, that would actually be a pretty interesting story. They could both develop in a way where they could agree that what the other person does is not bad, just different; they would learn that unity is better than conformity (and a villain in that chapter would be a reflection of that theme as well so we would get an interesting villain), so their attempts at trying to make the other the same would cease; and they could stop arguing with each other and focus on finding what they have in common. That story would be awesome.
Commonershipping: This is one I like just because I like the two characters in it. I would wait until they were older to actually put them together in any story just because they are still twelve. For a story that did feature them, I would suggest going with the classic Disney plot (pick love over money) and do it well. Remove the suitor antagonist, remove the parent's disapproval of the hero (Dia), and make the theme something like "a person is more than their social status". A major aspect of the story would be that some people don't like Platina just because she is rich and/or because she was born into wealth and did not earn it herself (like Maylene did in the comics). The main antagonist that would drive the overall plot in the story (whatever the writers wish it to be) would be the Galactic Commanders because they are awesome and they could be more developed as being the opposites/reflections of the Dex Holders they fought at the lakes. Platina would learn that her wealth is not what defines her (since the main theme is that it doesn't matter), Dia would learn that he doesn't have to be rich or famous to get her attention (ergo the theme again), and Pearl would be there because we would need someone to keep the other two involved with the overall plot (just like he unintentionally did in the comics).
Agencyshipping: This seems to be the direction that the authors are going with these two and they both complement each other really well. xEryChan, Black calling White "Boss" is not cute. It is done out of professionalism since she signs his paychecks. If he wasn't her employee, it would be weird and creepy. As for a story with them in it, I can't really say since their current story isn't even complete yet and we don't know if they will end up together at the end of their current arc or not.
It would be interesting to see White and Platina interact together though. Platina was born with her wealth while White had to earn hers. It would be interesting to see them fight over which is better, earning or receiving. This could lead to some good character moments and, if done right, we could see two Pokedex Holders work together that don't really like one another. They would only come together because they HAD to not because they wanted to. It would show that not all of the Dex Holders are goody-goods that all get along with other heroes. Something like that would humanize them.
Well, that is my two cents. I chose to only dwell on what would be the big shippings in the series because if the authors were to actually do this, it would make more sense from a monetary perspective (and I didn't want to talk about every shipping in the entire series and the stories they could tell). Personally, I think that these kind of stories would be interesting to tell and would be interesting to see, despite the fact that it could potentially cause some rifts in the fandom. Feel free to call me an optimist (if you agree with me) or call me an idiot (if you don't).