Those wondering why Fire Emblem: Three Houses feels so different from the usual entries in the franchise now have an answer: it's because the vast majority of the development staff actually came from Koei Tecmo. Intelligent Systems itself only had seventeen developers overseeing the project, composed of "a minimum crew of several designers, a music composer, and an adviser to the programmers."
In the most recent issue of Famitsu, they featured an interview with Director Toshiyuki Kusakihara of Intelligent Systems and Director Genki Yokota from Nintendo. In it, they discuss a myriad of topics related to the development of Three Houses - most notably, they mention how they outsourced development to Koei Tecmo, who had been developing Fire Emblem Warriors for them at the time.
Director Yokota states that they had initially planned to release a new game by the end of 2019, but had concerns about the time required for development. They decided to add "another developer into the mix" to speed things up: a decision that ended up influencing much more than the production speed of the game.
They reached out to Koei Tecmo, a developer most known for their empire of media franchises based off of the 14th century Chinese epic "The Romance of the Three Kingdoms." This historical novel mixes legend and myth with historical facts of the ancient Three Kingdoms Period, and is a cornerstone of East Asian literary tradition. A story of passionate tragedy, human ambition, and cosmic cycles of order versus chaos, this tale is the basis of Koei franchises such as Dynasty Warriors and Romance of the Three Kingdoms - and it seems that it provides the inspiration for the newest Fire Emblem game as well.
Director Kusakihara says that once they decided to work with Koei Tecmo, they had "considered their sense of world-building with three balanced kingdoms." The titular three houses were then based off of motifs from The Romance of the Three Kingdoms, as well as the plot taking the form of a tragic "long-form character drama." The length of the game was also enabled by the consistent production speed that the Koei Tecmo team was able to keep: at one point, the directors state that, encouraged by the "limitless" development skills of the Koei Tecmo team, they accidentally made the game twice as big as they had initially planned.
While not stated in the interview explicitly, fans can probably also attribute the gameplay improvements to Koei Tecmo's involvement. As a developer that manages several different long-running franchises with a variety of gameplay styles and mechanics, it's likely that they provided an expert outsider's perspective on how to combine Fire Emblem's best features into one streamlined experience.
It's unknown whether or not Intelligent Systems plans on continuing to heavily involve other developers in the production of new Fire Emblem games. Though, considering the success of this venture, it seems pretty likely - fans will just have to hope that it keeps working out in favor of game quality and not to the detriment of it.