There are always 3rd party games that I want to play on the handhelds I've owned, but they almost never come out in the first couple of years. Switch already has a lot of third party games that I want to play, and this is really supposed to be the slow period for third party games. It's about to pick up a lot, and already it has thousands of games. Switch is already on track to have the largest library of games of any console yet.

Other handhelds didn't have Bayonetta 3 or Astral Chain

Those are first party.

Platinum isn't owned by Nintendo.  How are those first party titles?

Nintendo's calling the shots. They own the trademark to Astral Chain, they're pouring money into development and marketing. It doesn't matter if Platinum is owned by Nintendo or not, the development team answers to them for this title.

Bayonetta is a bit trickier. Sega owns the Bayonetta trademark, but Nintendo owns the rights Bayonetta 2 and 3 under the license of Sega. 

It's good, but it could be better. It's definitively shaping up to be a great library, but it still lacks the amount of big JRPGs the 3DS had, not to mention the sheer variety the GBA and certainly the DS had. It's at least better than the GB at this point.

You are surely right, but as a casual JRPG fan, all I needed to hear was “Final Fantasy 7, 8, 9, 10, and 12” to make me forget all about 3DS.  I will also say that amazing 3DS rpg lineup comes at the cost of many other genres: I can’t think of more than 3 good racing games or platformers on the system.

I've always considered that 2nd party.  But it doesn't really matter.  For me 1st party is Nintendo developed.  

So all those RARE games published by Nintendo were actually first-party titles and not second party titles?

I agree with you there, but it’s so much more than that. If you take a look, you’ll see the nonsense in saying that any other Nintendo handhelds stand up to Switch’s RPG (or JRPG, if you want to call them that) library.

When you look at what’s listed on Metacritic as an RPG first two years and four months of DS, most of them aren’t even really RPGs, just action games with a fantasy theme. What can be considered a “JRPG”? There was this game called Contact and a remake of the NES game FF3j.

Are we really going to pretend that this stands up to the dozens of “JRPGs” on Switch which include: enhanced ports of FF7, X, X-2, 12. Disgaea 1 and 5, Tales of Vesperia, the Romancing Saga games (which I don’t think were ever released here before), all those 126 or so Atelier games, those Super Neptunia games, Langrisser 1 and 2, Ys VIII, and Oraclepath Traveller?

None of Nintendo’s handhelds had even close to the output of RPGs/JRPGs that the Switch has had. When you combine all (GB, GBA, DS, and 3DS) RPGs, that number not only falls short of the total on Switch, but it’s less than half.

I think people really aren’t aware exactly what has been achieved with the Switch. When compared to Nintendo’s handhelds, it totally stomps them. The Switch is 2 years and 4 months old, it is already WAAY ahead where any Nintendo handheld was at that point. In some ways, further than they’d ever reach.