I have seen a few free games that pull off a somewhat reasonable balance between microtransactioning you to death and being a fun game.
Stronghold Kingdoms is probably one of the best examples of doing a free MMO right. You either buy perk card packs to help your industry or buy premium coins that allow you to queue up research and build orders. So you pay to not have to constantly sit on the screen micromanaging everything.
Marvel Avengers Alliance 2, Marvel Future Fight, and Star Wars Galaxy of Heroes (surprisingly done by EA) are all fun games that give you plenty to do without charging you an arm and a leg to participate. I was competitive in the top tier of my server for Galaxy of Heroes and I never paid a dime. Granted, they offered bonus packs for the "whales", but they balanced that with generous options for free-to-play folks as well.
If EA can pull off a fun free-to-start app with options for reasonable in-app purchases next other whale packages, I have no doubt that Nintendo can do the same and even excel at it.
It would be cool to see the app be a "Fire Emblem All-Stars" title where you can recruit any heroes from past games. It would also be nice if they brought back the GBA art style and made the entire game sprite-based. It would be less graphics intense on phones and allow them to differentiate the app from the main line FE titles.