I answered yes only because there wasn't a "I haven't decided yet, but it might be" answer. I lean towards yes though.
I have not played every single game in the series, but despite it's flaws, Three Houses felt the most engaging to me. Fates Conquest gameplay was great, but the story was pretty shit and one of the worst in the series. Three Houses easily is my favorite story and characters in the series. The fact that it's from four different routes makes it interesting, despite part 1 being largely the same for all three houses, and part 2 reusing maps between routes. FE has done the split thing before, namely Fates (they were all completely different games) and Sacred Stones (different routes with different maps that eventually converge, but have the same cast of characters), and Gaiden/SoV. Gaiden had done that the best with being able to switch between sides at any time, and the maps and characters were different.
The monastery stuff I can see why people didn't like on subsequent playthroughs, and I had the same issues to a degree, especially on part 1. However I really liked the personality the monastery adds to the characters. Seeing things like choosing to give the item to Catherine or Shamir, and seeing them argue over it, was neat. The customization of characters was really fun, and my favorite thing about it is being able to optimize it on subsequent playthroughs when you understand how all the systems work. Overall I liked the monastery and academy setting as it added a way of bonding with the characters that isn't simply "marry them" or "have a silly conversation with them".
I think the difficulty left something to be desired. On my first run, playing on Hard seemed like a "normal" to me, but that got easier in my second and third playthroughs. I decided to do NG+ on my fourth playthrough (Blue Lions, not even to part 2 yet), and I regret doing that and not picking Maddening. What I had heard about Maddening (such as the moving Death Knight) made it sound more like frustration than challenging. Looks like I will probably be wrong there... My Byleth was able to one-shot (really two attacks, but in the same turn) the Death Knight on the second and third encounters with him in Part 1.
They are clearly onto a lot of great ideas in Three Houses, which I think they could easily refine and come up with an even better game. Three Houses was my personal GotY. It sounded like a lot of the development was done by Koei Tecmo... If this is what that partnership is capable of, I hope they continue to co-develop it with them.