I've tried deploying Warrior Monks and uh, they're not great :/ they're strong at first, but aren't readily available due to the limited amount of faith income in early game. When faith income makes WMs more affordable, they're likely outclassed.
The dream is getting Exploding Palms (+10 str) and Cobra Strikes (+15 str), but that basically makes WMs competitive with their environment given how long it takes to get WMs to 4 promotions. If you want a 60 str melee unit with more than 2 movement, there are easier ways to do that.
Victor and Moksha can help by giving free promotions, but it takes awhile to get to those titles. Victor isn't really a first pick gov, even if the free promotions are awesome. I guess Terracotta Army can help, but other units also benefit from TA and will eventually scale better too.
If you wanted to try making WMs work, I guess I'd recommend Scythia. Kurgans produce faith and are available early, so that makes WMs more affordable. The damage bonus and healing on kill will make WMs less squishy, so they can fight more often and gain more exp. Spain might work due to their str bonus against civs not following their religion, but I'm at a loss for other civs I would recommend.