Going to play the necromancer here and breathe new life into this warrior monk thread.
So I was around the forum and something I read triggered me to look into warrior monks. I read this thread, read some more around the internet, namely reddit. And I got this urge to play CIV VI (while i am still playing The Legend od Zelda Breath of The Wild btw) and I had to try a warrior monk domination game.
So I did and I am winning, I picked China with Qin Shi Huang, chose the East Asia map, just because I never played it before and unlike the true star version where you star location with China is really weak, this maps puts China start location, maybe dependent on leader idk, next to the Himalayas...so nice faith yields right from the start and eureka for the holy site!
I am playing on Emperor at epic speed, might try a later game at a higher difficulty and on standard.
The warrior monks are not that squishy and their cost is really cheap and always the same through the game, so you can spam them easy. Once the AI gets line infantry it gets rough but if you flank them with armies of warrior monks, they can get the job done.
I guess you don't need a faith civ if you have good starting yields and an early holy site to secure the first prophet and guarantee the warrior monk belief.