I've been really excited to play this comp for a while. Shadow priests have a near and dear place to my heart. It's what I played during vanilla and I think their aesthetics are really cool. After having played it for a couple weeks and doing a few mythic dungeons, I believe my take on it is that it's not the team you're going to want to play all the time and push with. It's a challenging team to play and they do a lot of damage, but it's not forgiving and sometimes I just want to login and not have to think too hard or be flawless.

-Amazing Cleave damage
-Has a fun, fulfilling kit with some nice toys
-Feels good and fresh

-Garbage AoE damage. While being able to do a ton of damage in burst windows or on 3-4 targets, anything beyond that is a nightmare. Mind Sear is fairly useless.
-Mind Flay can be annoying to work around. You'll need to use things like stopcasting macros for movement which is like another step.
-Damage is a little bit of a ramp process. You have really good burst, but it's not front loaded. A lot of trash packs feel like nothing for 10 seconds then all the sudden everything falls over.

Vengeance Demon Hunter
-5% extra magic damage debuff. I won't say this is required, but if you have 4 casters all doing 2k dps, it's an extra 400 dps for the group.
-Great mobility/survivability/self heals
-Kinda fun to play in its own right
-Not a requirement for this comp. You can bring your tank of choice. Definitely are going to want a tank that has good AoE damage to make up for the priests lack of AoE.

Shadow Priests
One thing I didn't point out in the video is that my priests are necrolords for the extra burst dot that also includes healing and another shield from fleshcraft.

My talent choices are here:
The only variable here is Surrender to Madness. I think good Surrender to Madness usage is really going to be what would allow someone to take this from being like a +4-+6 comp to being a +7-10 comp in Mythic+ dungeons.

I also didn't talk about legendaries. That's still a little up in the air.

Final Ratings
Ease: 2/5

This is not a super easy comp to play. The rotation is largely based around burst windows and survivability is not what it is on the other hybrid caster options (shamans/druids). A large part of being successful with this comp will be pressing the right buttons at the right times and having good positioning. There isn't much opportunity to recover from mistakes when they're made.

Versatility: 2/5
Not a versatile comp. You could use a priest as a healer for another team or use 2 priests for a mixed caster team, but otherwise you're probably going to just play 4 shadow. A shadow trinity could be viable. I'd probably bring in a shaman over a priest for lust right now though.

PvE Viability: 4/5
While this team is squishier than other caster options, I think they have a lot of opportunity for success particularly around their damage. I also think they're the best clothie option available.

PvP Viability: 1/5
I don't PvP with casters. IWT missing isn't great and even with Mind Sear and Mind Flay, facing with this team isn't as easy as I'd like to believe it should be.