I don't see that happening.
1. Despite having a full roster, like SB4, there doesn't appear to be much improvement. With Mario Kart, there was a TON of improvement from N64 to Wii; and while there was decline on the Gamecube, people recognized MK Cubed was a stop gap game with all its BS and sloppy design, and that the next real Mario Kart was the Wii version.
2. I don't think the fanbase expanded from Brawl, it seems to have peaked there. It grew between Melee and Brawl, obviously. With Mario Kart, a LOT of non-N64 owners played the game multiplayer, and those gamers later bought DSs and Wiis, and each of them bought Mario Kart.
3. The Switch demographic hasn't expanded significantly in the local multiplayer fanbase from the Wii, despite its increased capabilities for local multiplayer.
That all said, I would say Smash peaked on Wii, and it won't get above those numbers on Switch. At best it will slightly exceed them - and that's only if there's some kind of unforseen renewed interest in popularity. I don't think it'll be far behind, but 13M is a hard barrier, it'll be closer to 10 or 11M, and probably not for a while either, as many of those buys will be "down the road for my collection because I own a Switch" buys.
What kind of improvements are you looking for? Personally, Mario Kart is still Mario Kart with each installment and I mean that in a good way.
Besides adding a new system into gameplay, most fighting games don’t drastically change from the last installment.
I guess the big factor is that Smash Bros. is a fighting game. As of late, fighting games havent set the world on fire in terms of critical and commercial success, with the exception of MKX and, to some extent in sales, Injustice 2. Factors include companies getting in their own way like SFV launching with little content and bad netcode, issues with graphics and roster like MvC Infinite, or being niche like KoFXIV and ARMS.
Smash doesn’t appear to have any of these issues outside of maybe online (though I haven’t had much issues with Nintendo’s online). Smash has the one of the biggest fighting game rosters and is possibly the “biggest crossover in gaming history” as quoted by Sakurai. Plus, there’s bound to be more to be announced in terms of roster and other content. Graphics have shown improved rendering and most of the characters have been reanimated, even if they look similar from previous games. And it’s certainly not niche. If the Wii U game was able to sell 5-6 million on a 13 million install base, especially when the console had little to no momentum left in 2015, then how Ultimate only do a little better on a rising console that already passed Wii U’s LT sales? Switch has been marketed towards young adults, basically those who are likely to be attracted to such a game compared to the soccer moms and seniors from the Wii install base.
Plus, it’s a headliner for this holiday season along with Pokemon Let’s Go.