Yeah the replayability of Three Houses is incredible. The only real specific issue with it in this regard is the really really slow early game. Like, I usually have trouble playing the same FE game twice, preferring to jump from one installment to another in order to keep my experiences fresh. However outside of the painful experience that is trudging through the early game again, I actually rather enjoy playing Three Houses multiple times in a row. Which says a lot, at least to me. Anyway there's nothing wrong with getting sucked into constantly replaying the same game over and over, if anything that just means its probably a pretty great game.
Oh, and not to go off topic at all, but if you are interested in trying out past games, be it the 3DS titles or the older games from before Awakening, be sure to keep in mind that majority of Fire Emblem games are quite different from one another in terms of writing, gameplay, and overall experience. Three Houses in particular is a good example of this as it is very much its own thing due to how it modified different mechanics and brought back various elements from past games. Based on what you've said on your experience with Three Houses, I suggest looking into Fates Conquest and New Mystery of the Emblem. To keep it brief: Conquest has challenging but rewarding gameplay and New Mystery has huge replay value due to its reclass system as well as amazingly scaled difficulties.