If you sincerely believe that this company is petty and spiteful enough to deliberately undermine their first attempt at a similar initiative to what you're describing I don't even know why you think them handing the holiday reigns to some spinoff is even a possibility worth dignifying
Not if there was a point in it. And that point: Only GF can make a main series Pokemon game. When you compare the the job ILCA did with BDSP to any of the recent main series Pokemon games GF has done, well the ones GF made look like masterpieces. Clearly, from this one instance, GF are the only ones who can a main series Pokemon game and no one should ever doubt this or think otherwise, especially The Pokemon Company or Nintendo.
We just gotta ignore that ILCA isn't a major developer or at least on the same level as GF (only seemingly picked because they've previously worked on Home), that either GF or Masuda forced them to work with the old DP code (but not Platinum) and not to change anything unless absolutely necessary (or was something that GF didn't care about like opponent movesets and post game stuff), and probably a bunch of other nonsense restrictions/limitations such as no Pokemon from Gen V+ and having to work with this strange art style of replicating the 2D graphics in 3D (and not allowed to redesign the characters or introduce new ones; which wasn't a thing GF restricted themselves to with other Remakes (aside FRLG's strange no non-Kanto evo until post game side quest)). Heck, they weren't even allowed to bring over the Contest Spectaculars from ORAS, they had to dumb down Super Contests into a simply rhythm game.
However, side games are a different thing altogether. Many don't use the same gameplay as the main series does, more focused on using the Pokemon and few connected mechanics (Type Chart mainly) to build a new game upon (or adapt a Pokemon skin over). Sometimes these games help in the worldbuilding of Pokemon, but just as much these games are just meant to be a fun experience. And in doing so it shows the Pokemon franchise being flexible, that Pokemon are more than battling or battling isn't restricted to a turn-based system. And while I'm sure GF has plenty of side game ideas, they also aren't worried a side game made by a 3rd party is going to reflect on them negatively. If a side series does good, great, that's its own thing over there in the corner which is making The Pokemon Company some money. But if a 3rd party proves they can make a competent, if not good, main/core series title as GF than GF isn't looking as that hot of a developer anymore.
Or, if you want to look at it in a less conspiracy way, could be GF just didn't trust ILCA enough to make a main series to make a main series game without a blue print to follow. Of course, if that's the reason why, then why didn't they get a bigger studio known for making RPG games like Monolith Soft or Square Enix. "Maybe they wanted to work with someone who had worked on a Pokemon game before". Okay, then, Koei Tecmo made Pokemon Conquest and Bandai Namco made Pokken. Or if you want someone familiar with making a game on the same vein as the main/core series, Genius Sonority is still around (I don't think they would have mind taking a break from Cafe Remix).
Console spinoffs are cool and we could use more of them, it's just that we should think a bit outside the box and ask for some new stuff.
I was just listing known examples, when it comes to spin-offs I would think most anything (as long as child friendly) is on the table.