The Archimonde situation is an interesting one. Soaking the doomfire is well suited to healing priests thanks to the constant 30% damage reduction from focused will and the extra 10% from glyph of fade, however I'd have to argue that being disc and holy would (or should) work out better than double disc. As disc you can keep yourself alive through doomfire, no issues there, you each look after yourself and it's easy life. Outside of the soaking however you meet the usual compromise of nerfing each other. Indeed my example of shielding shackles on mythic when overlapping with chaos, they're priority targets and while you could have CoW con them, you're still doing less than double what a solo disc priest can do. A holy priest ALSO has 30% focused will and glyph of fade and binding heal and lightwell is incredible strong at healing doomfire.
As a disc priest soaking doomfire and looking after themselves you're forced to either flash heal or CoW yourself or blow CDs to survive bad luck (bad luck being if you take a shadowblast thingy or get dogs on you), and you can only PWS yourself. If one of you went holy then you could PWS BOTH players, which increases efficiency for the disc priest and the holy priest can use binding heal with rolling renews in serenity chakra, also more efficient, not to mention PoM bouncing between soakers can be extremely strong and lightwell as a backup (click it!) is also very very strong. I don't think double disc is required to soak doomfire and indeed I believe that if organized correctly (so PoM can bounce), a disc and holy would actually be the safer option for soaking.
The next point in the fight where your healing comp would actually matter would be mark of the legion and infernals landing. As double disc you could certainly be sure to pre-shield the whole raid, a legitimately valuable tactic. However if all marks are equally soaked then nobody is really in danger of being 1shot anyway, and if you have 1 mark being undersoaked (say only 2 people soaking) then again only 1 disc priest will be able to shield them and then you have less throughput to top them back up for the infernals landing afterwards.
In a scenario where you have 2 healing priests regardless then I'd expect to see a situation such as; 2 disc priests doing 70k hps, wasting mana on inefficient healing (flash heals) or wasting hps on less effective spells (casting a CoW on a target that the other priest put PWS on). If it was one disc and one holy priest I'd expect the disc priest to be doing 90k hps and the holy priest to be doing AT LEAST 70k hps, obviously these aren't numbers taken from real-world, just my expectations for comparison. And yes, the usual caveat that if you're healing up all the damage anyway then it's really not going to matter; this whole topic comes to a close if you don't actually need to improve your raid healing.
I do believe that double disc is viable (and proven to be viable) but I also believe that it's never optimal even when forced to have 2 healing priests. Obviously if you could just drop one and bring another class entirely that should be even better (holy paladins soaking doomfire is really good too!)