yeah I've often thought about taping one of those bluetooth transmitters to the back of one but never bothered with it lol
also if you have to ask what games are worth having a 3ds then the 3ds is probably not for you, pretty much rpg fans and nintendo fanboys [as myself, when I wore a younger man's clothes la da da...] and so basically if you're asking this question either go vita or just run games on your phone, I mean a switch is cool but half the library's prob gonna be similar I'm a cheapskate and haven't looked in to the switch too much yet, pokemon snap be calling me tho haha
Even though it's a DS game, Pokemon Platnium would be a good option. It's one of the longest of the series' games, and its challenging compared to the other games. Not to mention, there are a lot of optional rules that can be added to make the game replayable hundred of times, like I have.
If it has to be a 3DS game, I'd say play Mario Maker. You can be creative, or rip your hair out over other people's impossible levels (like I do). Personally, I come back every day to play either Animal Crossing: New Leaf or Nintendogs + Cats. I like virtual pet games, and Animal Crossing is just kinda fun for me.
A few good 3DS games are Tomodachi Life and Miitopia. Both are amazing and fun 3DS games (though Miitopia can only really be played once before it gets kinda boring). Both were so well made, and I think it's anazing that some of the best Nintendo games were based off characters that were basically only used for avatars on the Wii.
In the end, it's just personal preferences. I've always loved the Pokemon series, and own all of the 3DS titles, because there's so much to do!
The only game that I go back to my 3ds is The Binding of Isaac. To clarify I have own a 3DS for a decade and enjoy some of the games enough but lately I felt they're not worth my time. I said I go back to Binding of Isaac because of the replayability and complex it is.
I generally play Tomodachi Life on and off from time to time. Don't get me wrong, it's one of my favorite 3DS games, but I always tend to put it down after a week. I just kind of wish there was more content in the game to keep it engaging, but it's still a great time-waster for me.
I'd say most RPGs are worth checking out including Kingdom Hearts 3D Dream Drop Distance and Bravely Default series.
I played a shit ton of games from that console including Monster Hunter, Resident Evil Revelations, Kid Icarus, Metal Gear Solid 3, Luigi's Mansion 2, Professor Layton, and many more. Aside from those games, I still have a backlog of it. 3DS is definitely worth it especially if you're into collecting, otherwise just pick one console either 3DS, Switch, or even the Vita. If you're into current generation games, then Switch is great. At the end of the day, it's up to you on what games or genre you're into. I could just easily jump right back in and spend more time with Monster Hunter.