This may not be on Game Freak's part (at least when it comes to Smash) but the Pokemon Company. I'm watching Chuggaaconroy's Let's Play of Yoshi's Woolly World and, for that episode's Amiibo wool Yoshi pattern, he scans in the Pikachu Amiibo... and it came up as the generic Yoshi Amiibo. Turns out, NONE of the Pokemon Amiibo gives Yoshi a pattern to look like them. They have a costume for Mega Man and Sonic, properties Nintendo doesn't own, but not for Pokemon. And this isn't the first time something odd like this happened. In Mario Maker, while it does have sprites for Pokemon characters, they use generic sound effects while every other character uses sound effects from their game series. Animal Crossing is filled with references to Nintendo's other popular games... except for Pokemon (it wasn't until the Animal Crossing spin off, Pocket Camp, did they get anything Pokemon-related and it was a few day Event advertising Let's Go with only furniture based on Poke Balls and Eevee).
Now, according to Chuggaaconroy, the reason for at least the Woolly World exclusion is because the designers couldn't properly represent the Pokemon characters via Yoshi's shape. However considering every other Amiibo character (released before the game) has a Yoshi pattern this is rather a weak excuse. While not finding anything official,
there was a Reddit thread originally leading to the same article I assumed Chuggaaconroy read and what I get from the comments is that the blame may be more on Pokemon Company being very over protective of the Pokemon property. Seems like Pokemon Company's leading philosophy is that if Pokemon isn't taking center stage, you're getting little if not nothing from them.
There's no Pokemon costumes in Yoshi's Woolly World because the designers couldn't properly make a design that Pokemon Company would approve of.
There's no Pokemon sound effects in Mario Maker because they're only making a cameo appearance with all the other Amiibo characters. Infact the only reason they have anything Pokemon is because it's a Mario game and they would look bad not giving them something.
Animal Crossing gets nothing because anything Pokemon would be a super casual cameo appearance. Only reason Pocket Camp got a Pokemon Event is to advertise Pokemon Let's Go (Eevee). And while they could have only done it in Pocket Camp is because it was the latest Animal Crossing game out, considering the apparent pettiness TPC is showing they allowed it for Pocket Camp because it's a spin-off of Animal Crossing thus not have as many players as a normal Animal Crossing.
This leads us back to why Smash only has music for the core series, why do the games not reference many of the spin-offs, and the anime has a notable presence in the games: if Pokemon Company (or Game Freak, they're complicit in this too) doesn't directly control or oversee it they prefer to keep it its own separate thing. They may contractually own the spin-offs, but since GF didn't make it its not considered part of the Pokemon's brand vision. The anime is a special case as it's controlled by the Pokemon Company and it pushes merchandise more than the spin-offs do. That could also be why you don't see Pokemon Special/Adventure manga referenced that often either; while critically praised as being better than the anime it not only doesn't push merchandise but also because it's published by
Shogakukan, a Japanese media distributor.
Trying to put it in an analogy, let's say the entire Pokemon franchise is like a tree. GF and the core series are the roots. TPC and everything they have complete control over (such as the anime) are the trunk. Finally the spin-offs, manga, and even the non-main anime shorts (Origins and Generations) are seen as branches. The branches obviously connect to the trunk (what TPC controls), but they (theoretically) do not intersect with each other. In addition they cannot exist without the trunk, but the trunk can exist without them so it does not need to be concerned with the branches. Meanwhile the roots (GF and the core series) keeps on doing what they do, only really interacting with the trunk/TPC.