Dragon Quest IX was immensely popular, and one of the most successful Dragon Quest games in the history of the series. Not just in Japan, mind, but I knew scores of US players who were always looking to link up and rock multiplayer, DS-to-DS. It was a social game before StreetPass and mobile titles really took off. Everyone needed a full copy of the game to play, a concept that helped it smash sales records.
It was also a pretty good game, and that's why we're talking about it a decade later. Square Enix is talking about it too, as they just hosted a special Dragon Quest IX 10th anniversary livestream, which touched on the idea of bringing the game back to modern systems. Although the mobile platform is an obvious choice, given that a ton of Dragon Quest games are on it already, Switch was also heavily discussed, with, according to Siliconera, roughly "80-90% of its playerbase" asking for it on Switch.
In typical Square Enix fashion you'll need to beg for it, as co-director Jin Fujisawa has requested that fans keep noting interest: as they have been for nearly 10 years. Level-5 CEO and Square Enix buddy (seriously, he shows up at a ton of their livestreams!) Akihiro Hino says that it could take "about a year" to make from his end if it was a straight port.
As Siliconera points out, the team notes that nothing is confirmed today, they're just talking about the idea. But Square Enix is Square Enix, and they have a nice collection of "smash glass if profits are down" modules, and Dragon Quest IX on Switch would make a pretty penny if they ever needed it.