It's not "cherry-picked". Fact of the matter is, Pokemon doesn't treat its overall starters as equal. It consistently has ones more important than others. And last I checked, Incineroar is significantly a bigger deal than Decidueye. One is involved in a movie as a major character, is treated as very important in the anime(unfortunately the birb is not given much at all. Rowlet slightly, but that's like the only form notable there at all, with Decidueye having a minor appearance at best. Incineroar is given way more importance, even before becoming a main Pokemon among Ash's team).
It's absolutely a good reason. There's no reason to choose any Champion because none stand out from each other as important. None are pushed. They already play minor roles in BOTW to begin with. Which isn't helping. It took what's essentially a spin-off to even slightly make one stand out, and that's due to bias from a third party, not Nintendo nor important advertising. One will stand out as soon as Nintendo thinks it's a good idea to make them that way.
...Which can't be said for Pokemon. Cause, again, yes, they do treat some as more important than others. That's how it's always been. And how it has to be because the anime is a big part of the franchise and they can't give equal screentime to all 3 final forms effectively(and never have once). Considering Ash-Greninja was added to the games too, they already had pretty much considered him much more important. It also doesn't change what I said about Primarina pretty much having nothing to go by, with Decidueye getting some importance, and Incineroar easily leading the pack by far.
You'll always find tiers. Anyone thinking Swampert is remotely treated like Blaziken or Sceptile is pretty much being ridiculous. While not every Gen is bad about this, a lot tend to always have a frontrunner or ones who are clearly more important. That's just how they went about it, giving some more importance than others. Especially when one becomes Ash's Pokemon, who is the main character to begin with. That automatically puts them in an immediate higher tier of advertising.
I'd love it if they actually made an attempt to make other Zelda characters notable beyond their own game, or at least took the time to properly flesh out a group to help them stand out. Unfortunately, the formula rarely allows for that. We barely had it in MM with letting you play as other races. And you're still Link. Hyrule Warriors hasn't really influenced anything, since Aonuma pretty much wasn't up for letting Zelda be playable alone. Silly, but the core point is there's no actual reason to believe that they'll try to push another race member, especially the Champions, into some tier within themselves. There's nothing to gain from it on their end. They already marketed them as equal, wanting them each to play a minor yet important part within BOTW itself.
Let's also note Blaziken even more; it's the one deliberately used to advertise Gen III at the end of Johto. Let's not forget Infernape, who was vastly more important than the rest in the anime yet again. It is possible for them to kind of make them equal... if the anime wasn't a thing, where there's always an advertised favorite. Gen V? ...Yep, hi, fire starter. And the other ones weren't even given much to begin with, as they weren't a core part of Ash's team in the same way. Samurott's core user was a one-off random guy just to knock Ash out of the tourney(Cameron. Albeit, Lucario did that, but that's not the overlal point). I'm also trying to remember exactly what Gen VIII Starter isn't really given much focus in the latest anime... oh, right, the Grass one. Fire and Water are given a pretty good amount, but Grass? Tis on the eh side. Hell, Grass somewhat often does get the short end of the stick, but regardless, yes, there's a very clear bias by Gamefreak(and maybe part of it's Nintendo) to not treated them as equal. It's severely rare, and kind of stops being a thing in the anime. If you're lucky, you get 2 with somewhat equal footing.
