If you've never played a Luigi's Mansion game, and you own a Switch, you should definitely pick it up.  It isn't something that I'd really factor into whether or not I buy a system, but it is good enough to warrant a purchase for a system I buy for other games.  

IMO, Switch is worth buying if you're really into the Nintendo core franchises, and won't have to stretch to afford it. If you didn't own a Wii U, there's more reason to get Switch. If you do have a Wii U, about half of the big games are available there.

As I've written elsewhere, my Switch is mostly collecting dust because they haven't released enough new stuff in their core franshises. Zero exclusive Zelda games and no new Mario Kart are the most obvious omissions.  There's also no new 2D Mario, unless you count Mario Maker.  

Nintendo milk their fanbase with re-releases, the key serecet to enjoy Nintendo is to buy on hardware and skip the other :p 

Well there are 4 switch exclusives that I consider exceptional:
Breath of the Wild
Super Smash Bros. Ultimate
Astral Chain
Super Mario Odyssey

Sort of obvious picks except maybe Astral Chain, but they really are the best ones in my experience.

Better question is not why get it? Access to some of the best games of all-time anywhere you take it, including not just Nintendo franchises.

I've always been an early adopter of Nintendo systems. But, I think those days are over for me. Going forward, I'm going to wait several years before purchasing Nintendo hardware to make sure that there is a sufficient catalog of games that I have not yet played. When we get to that point, if it looks like the next gen hardware is coming soon, I may well do as you suggest and skip a generation.

I really feel like Nintendo has not done right by those of us that were loyal and bought the Wii U.  We get to play the same games again and pay full price for them.  At the very least, they should have offered some sort of trade-in program where you send in your Wii U disc and get half price access to a digital Switch version of the game, or something like that.  For that matter, they could have just sent out discount codes to anyone that played the Wii U versions of the games prior to their release on Switch. Nintendo certainly has that information for the vast majority of us. 

If you missed them on the WiiU, play Mk8 and BOTW. Those 2 are the essentials. Mk8 Is IMO the best game the Switch has.
Other than that I heavily advice Astral Chain, Smash Bros U and I guess you could give FE Three Houses a go.
Links Awakening remake is nice if you can find it at a price cut.
Octopath Traveler is a must if you like classic RPGs, which I believe you do.

I cant say much for Mario/Luigi games since I personally get bored with them, Odyssey and Mansion 3 were no exception. When it comes to Pokemon, I personally consider sw/sh the worst main line games in the franchise and that is no exaggeration, but they are divisive games nonetheless, so you might have a different experience than I did.

Edit - Not an exclusive, but its only available on Switch and PC: Hades. That game is so good. 

First bold: if you already have the game on Wii U and don't want to rebuy it, then simply don't rebuy it. The Switch versions are for people who don't own a Wii U. Those are new games for them.

Second bold: Has something like that ever existed in gaming?

Links Awakening remake is only on Switch

No Virtual Console, and it sucks.
Closest thing is streaming NES and SNES games as long as you're subscribed to Nintendo Switch Online (a garbage service). Even the Wii and Wii U had digital N64 games. And I want them to finally give us GameCube games.

Animal Crossing: New Horizons, Fire Emblem: Three Houses, Super Mario Odyssey, and Super Smash Bros. Ultimate are pretty essential exclusives. Luigi's Mansion 3 is up there as well. The Legend of Zelda: Breath of the Wild is also on Wii U, but you might not have a Wii U. It's a pretty flagship Switch game.