.....why the HELL would they do something stupid like that? Interest in the "modern military FPS" seems to be dwindling anyway, so there's no point. CoD has continually been selling lower entry after entry, with no sign of recovery. And that's before we get into how the current big FPS' that are being pushed aren't military FPS'. Battlefield has gone in a cops and robbers direction with Hardline, CoD itself has gone near-future with more sci-fi elements, The Order: 1886 is a steampunk romp through London, Destiny is a space opera, Far Cry 4 is more a survivalist sandbox, etc. There's little point in doing it now when people have seemingly lost interest.
And then we have the fact that Nintendo isn't interested in making those types of games anyway. And they're publishing their titles that have a unique spin on the shooter genre. Devil's Third goes completely bat-buggering insane with over-the-top violence, whacky multiplayer modes, extremely eccentric character design, and interesting systems with melee, swordplay, and gunplay. Then we have Splatoon which uses bright, colorful presentation, shape-shifting squid as the characters, and the focus not on shooting your enemy, but instead literally painting the town red in order to gain territory.
This is the thing nobody who doesn't pay attention understands about Nintendo: they are not reactionary. The thing is, they refuse to jump into trends because there's no telling if something will last. And considering how the military FPS is burning out, they were correct in NOT lumping themselves into that. If anything, they react the opposite way. Instead of making a military FPS, they create a wacky paintball game. People obsessed over being as real as possible, they go as unreal as possible. Designers try to push their increasingly pretentious stories, Nintendo goes all-in on razor-sharp gameplay and design. And of course, instead of just making games that everyone else is, they choose to do embroidery-inspired Yoshi spin-offs, claymation-style Kirby games, a steampunk strategy title taking famous historical and literary figures from the 19th century, a game that lets us finally make our own Mario levels, and an open-world sci-fi RPG with MECHS. That's how they do things.