3 Monks

Monk is really clunky for boxing. There was one boxer here that had tons of success playing 5, you could probably find some old info they posted. Maybe they overcame my own shortcomings.

--Brewmaster isnt so bad, as in that you can do well without playing it to its maximum skill with the right spec, and is very boxer friendly for aoe farming. Ox-Statue is god-tier for aoe farming.

--WW rotation requires a bit of attention, hit combo, mastery, and building combo points makes it very boxer unfriendly. If you mess up hit combo, you might as well just respec as another brewmaster because your damage will be that low but your survivability will be like a paper bag. This is why i avoid WW boxing at all cost, they cant be left on auto and they have no formed out rotation, it's a priority that can't be botched, cause if you hit that whammy, you're a waste of space. If you can mash out a decent priority macro sequence while managing Tiger palm so it doesnt repeat, then you can have good success with WW.

--MW imo (i've seen others say differently so dont be afraid to get a second opinion, i mained monk during Legion and BFA raiding when not boxing) is now terrible for boxing. It was amazing, until they overhauled the spec in BFA. You could box it to maybe 60% effectiveness, and possibly 80% if you drove from the MW.
Lets start off by saying the clunkiness mainly comes from having to Empower your heals with a buff (Thunder focus tea) in order for them to not be terrible. Also, most of your healing is based on having buff procs you apply with other healing spells.

Renewing mists is a smart heal hot, it was amazing, but they gutted it in the overhaul and it heals for very little while acting instead as a proc buff for vivify. It's nice that you dont have to place renewing mist on anyone specific, it will find the lowest health bar after on GCD, but if you cast over a previous renewing mist, and you could accidentally do this because they bounce around a lot, then it overwrites it and the original is gone, which is terrible because you want as many bouncing around as you can get, to make your vivify AoE splash heal on them. If you renew on CD and pre-hot before pulls you will keep about 2-3 up on average.

So vivify is terrible unless you spread renewing mists on the group constantly. Thankfullly renewing mists smart heals to the lowest health bar, but with spikey damage it's rough.

Soothing mist is a channel that can make your heals instant cast, but that's pointless when you have to spend a GCD on soothing mists to get the instant cast after, and channeling is bad for mobility. The fact that it's single target ruins it's usefulness in a group. If soothing mist worked more like a channeled shaman chain heal and instants could be cast on all player chained, then it would be amazing and MW's everywhere would rejoice, but yah, it's pointless for anything beyond duo.

So to sum it all up, every meaningful spell you cast pretty much has a per-requisite spell in order to reach the usefulness that other healers get in a single cast. If played well, MW throughput is great, but if you half ass it, it's terrible because you're not getting the throughput without the per-requisite buffs.

And i havent even mentioned the worst thing about MW healers. They have the absolute worst mana efficiency of all the healers. You will be drinking almost every difficult pull, and that includes using Thunder Focus Tea buff on your vivify's, which is considered the best option in most situations.

Maybe 8.3 buffs fix all of this, i'm not sure, but as far as i can see they are just adding more healing power throughput, which MW already have enough of. More healing could help with mana, but i suspect it will just cause more overheal and no change with mana when you need it, and we'll likely see lots of MW's complaining shortly after 8.3 and a new buff added.

If i had to box a MW, i would take mostly passive fire and forget talents like invoke chi-ji, and i would run a rotation something like:
Renewing mist on CD
Essence Font right before any aoe damage
Spot heal with vivify
Big single target consistent incoming damage moments you should use Envoloping mist

Use Big cooldowns like
Chi-ji on boss fights
cocoon almost on cooldown
and revival anytime you have 3 people below 25%

Playing like this you could do any content that wasnt highly challenging.

As far as synergy goes, i dont think there is any with the 3 different specs, and they play so differently. You could fistweave with the MW, but it's so terrible and mana inefficient you'd likely only enjoy it for doing things like world questing. Sorry, i dont mean to be so negative towards the comp, it's just that the MW design is horrible atm. It was clunky before, and then they overhauled it and made it even worse. WW damage is like feral druid, the rotation takes solo focus and it bounces around from being viable or worthless. Brews are always great for tanking, but they dont self heal well like all the other tanks and they mess with your anxiety because their health is never topped off.

k sorry im done. I guess my final thoughts on whether or not to play this comp is a resounding yes, because Monks are cool as F and that's all that matters in the end.