[WoW] composition question

Prot/MW/BMx3 is one of the three comps I've currently got running at max level and I can confirm it functions perfectly well. I've cleared all Mythic +0 dungeons with it and I have no reason to believe it won't function well into Mythic Plus.

The BM Hunter DPS is a solid choice that will remain a solid choice throughout the expansion. Mobility is number one; without being able to function on the move, there are dungeon bosses that will be frustrating blocks on progress. There are a couple of alternatives (Balance Druid with Power of the Moon azerite trait, Affliction Warlocks), but I would consider the BM hunter the safest option that will remain a strong performer in all content throughout the entire expansion.

You have a reason to be fixed on the Prot Paladin, so I won't try to sell you hard on anything else. I've now tried three tanks at max level in BfA, Prot Paladin, Blood DK and Vengeance DH, and the prot paladin is probably my least favorite. The margins are fine though; all of them perform well, each of them has specific fights they make easier, none of them have fights they can't handle. Prot deals with Tidesage Council particularly well; I suspect this will be a gatekeeper fight on Mythic+ as the outgoing AoE damage is very high without access to plenty of interrupts.

The Monk is a very easy to setup healer that functions well. MW Mobility is good, not great; you look to essence font to do some of the heavy lifting in mobile situations with high incoming damage but some of the eccentricities of how it functions in 5 man content makes it considerably less effective than it looks on paper. As such, there were a couple of moments throughout the Mythics that I was thinking "Gee, I wish I was on my Resto Druid, this would be easier". Some of the utility the MW brings, however, is incredibly useful, including the best AoE stun in the game and access to Ring of Peace on top of that, which makes many trash packs considerably easier. In addition, they bring the Mystic Touch debuff, which will increase 100% of the damage the BM hunters deal by 5%, now that BMs exclusively deal physical damage rather than the hybrid nature/physical damage they did in Legion.

I think there's an argument to be made for all healers, but the chief competitor is the resto druid. Its harder to set up as you can't just use a gnomish sequencer macro and call it a day, but if you get it working the mobility is exceptionally helpful. In particular, I've seen good results using the Autumn Leaves azerite trait. Its not supposed to be optimal for dungeon content, but its first order optimal for us: just keeping a single rejuv ticking on each character with a Photosynthesis-ed lifebloom on the healer or tank depending on the situation and using Swiftmend to handle spot healing is enough to keep my team up throughout the mythics.

I'll also give a shoutout to Holy Paladins, who have respectable mobility, are reasonably easy to set up and can output a staggering amount of damage when they don't have to do any healing with Holy Avenger and Sanctified Wrath.

So there's a couple of thoughts to mull over, but summary is that your suggested comp is completely fine for objectives 1, 3 and 4. PvP I have zero experience or interest in, so I'll have to let somebody else give advice with that.