I highly doubt it as afaik no gem or set bonus influence your secondaries, and the effects are fairly generic. It’s all about dmg, primary stats and healing.
You may perhaps need a specific set bonus for a given spec but honestly it seems pretty clear cut & unless the balance is all over the place I doubt you’ll need multiple sets for your specs.
Perhaps a guide could give you a more accurate answer, as they should have a much better idea than me on what’s optimal.
There’s only 1 slot available from the open world and all 5 forms the raid. Gems themselves are obtained from the raid and upgraded from a currency earned in the raid. (4 or 5 tiers, with the last being iirc about twice as powerful as the 1st one)
So if your BIS gear for your favourite content (beside raiding) contains domination shards/gear then yeah raiding is mandatory.
That said I actually don’t know if PvP will really be affected as they actually did nerf the system in PvP : gems will be 50% effective, the set bonus won’t apply and gear may not have versatility (I honestly haven’t checked but raid drops don’t usually have it).
Oh yeah and PvP gear has a wod-like feature, being ~6ilvl below the equivalent PVE ilvl but receiving a +13 ilvl buff in a PvP setting. This, combined with the previously mentioned nerfs, could perhaps spare you from that feature.
I’d suggest you check a PvP community/discord/guide about it tho, Blizz has set multiple precedents of providing broken PVE systems messing with PvP. I do hope I’m wrong but you never know…
From my casual PoV the entire thing should’ve been raid & open world only, a lot of M+ players will have to go to the raid for either the unique weapons (legendzry hunter bow for instance, with an AOE silence which should matter more in M+ & PvP than raiding…) or these socketed items.
This is Blizz setting themselves for failure in an attempt to push us toward running their raid & doing the world content. Undoubtedly effective but players are going to hate it.