I wouldn't trade in your old systems for a new game and Switch. I guess it depends on how attached you are to your older games, but you're talking about trading in items you have an emotional attachment to for a new game that you could always pick up later. You won't be able to get those original files back, even if you rebuy the games. And Pokémon games can become hard to find (though this doesn't seem to be as big an issue for the 3DS games as it was for DS and GBA games). I'm also not sure if you could ever access stored Pokémon in something like Bank without a 3DS, which is another issue if you are at all attached to your collection.
Then there's the issue of how you feel about what you've seen of SwSh. Personally, I've been disappointed by some of the decisions that have been made (Dexit, etc.), and I would want to be able to return to older games to balance that out. But I also tend to be highly nostalgic, and like coming back to old games years later. You're the only one who knows your personal tastes, how you feel about SwSh vs. older games, and how often you tend to return to older titles.
Also consider what sort of deal you'd be getting. If you have to sell your old system and a whole bunch of games just to get the funds to buy a Switch and one game, that's a fairly large trade off. Do you have any other funds that could pay for part of the Switch + game purchase, or are you planning on funding this solely through selling other games and systems?
Also, have you sold old systems and games in the past? How did you feel about it?
I've never been one to sell old systems and games, and I would never personally consider it, which tells me that you probably have a different mindset and priorities than I do. So as others have said, you need to weigh what's important to you. But I will add that the most common regret I've seen mentioned on gaming forums when people reflect back on their habits is selling old systems and games in order to afford new ones. Thus, if it were me, I would hold off on buying the game and system for a few months, continue playing older titles, and then buy the new system once I had enough money saved up, even if that took me a while.