Maybe I need to clarify: I would rather stack intellect than being forced to use the whole Hymn of Hope. Of course the Hymn has it's use, but as long as there is a way to have enough mana (meaning the regen options are used correctly), I would not want to use the Hymn of Hope.
Obviously in Situations like Mimiron or Yogg-Saron where you have clear phase changes that give you a small break, using Hymn of Hope is the correct choice - I just wouldn't impair the time I can use to heal in favor of casting the Hymn.

For me personally there have been two main reasons to put in some intelligence gems: One is the double use for discipline and holy: I did not want to switch every part of my gear when I switched to holy - raid healing, and as holy I was having some issues with mana when spamming Holy Nova or Prayer of Healing.
According to my estimations it would be better to be able to cast some more PoH instead of adapting my holy playing style and since spirit is not that good for discipline, I opted to gem int and gain some crit and some flexibility.
While it might be subpar for one of the two talent trees, I see intelligence as a good choice in pieces that are used in both trees.
The second reason might be slightly less convincing: I have a paladin friend with whom I heal a lot, and I we developed a little game to see who would have more mana. This is not a question of what stat is better but rather a question of playing a little game and fooling around; just as tedv says: It's possible to beat even the more difficult encounters while not optimizing every little thing. The most important part is having fun while doing that

Why completely swap all int gems for all sp gems?
I've found a fairly good mix of using abuot 50-60% of my gems to be luminous ametrine, 12sp+10int. Keep the happy medium, building up your throughput while still keeping the buffer of your mana pool in case a fight goes downhill. As a healer in my raids though, I bounce around from raid assist, tank assist, to full MT healing, so I feel I need to be ready for whatever the days fight/raid composition will be.

I have started slowly dropping int, since I was sitting around 37k+ buffed in raids, and started gemming more strongly towards spellpower. If you end a fight with extra mana, try regemming one or two sockets, don't head to the opposite extreme only to find out next raid that you're ooming mid fight.

We are a 25-raid casual guild, with 2 raids per nights. On off-night, there is often 10 man raids, on voluntary bases. That means that we don't have optimized or stabilized groups. I can be with 2 druids, as well as with 2 paladins. I can be also required as dps.
For that reason, I choose a flexible holy / shadow dual spec. I took most of the "I can try to tank heal" talents, including divine fury and 4/5 empowered healing. When I'm raid healing in 25, these are nearly useless. The choices were not mandatory talents (spell warding / desesperate prayer / healing prayers / blessed resilience / body and soul : I can find use of them, but I can raid without them), and these GH-talents are useful when healing the tanks (or helping for it) in 10s. I can definitely remember tank-healing on heroic beast in ToC10, and that was tough enough.

I know I could be disc + holy specced. But I wanted to be able to dps sometimes (at least for questing), and my guild find use of my dps off-spec (some of our healers have a PvP off-spec, or no stuff for their off-spec). I could also be disc + holy, but when I'm required to raid heal as disc in 10s, bubble spam is not sufficient, and the flash heals I can throw feel very weak (partly because of the lack of grace).

Although I agree with your spec changes I do not agree with the gemming changes. Like stated many times before 'if you dont have mana issues or if you still have mana at the end of the fight then you're (A) doing something wrong or (B) Have too much mana for your healing style. I can't really relate with disc priests who ever say that they have a mana problem. I'm gemmed mostly SP and SP/Int and have not had any problems with mana. I come very close to 3400 Spellpower as disc (Raid buffed) (which is comparable to a geared holy priest). Shields absorb more and heals hit harder, all the same time having enough mana to last the encounter. I still believe that SP is the way to go, Priests have so many mana regen options with HoH, Mana pot, and Shadow Fiend. If used correctly you should never have a problem with mana.

If you're tank-healing, and you don't have any mana trouble, then you want to gem for throughput. This includes spellpower, but also haste and (most likely marginally) crit, which are also great stats to tank-heal.

I personally don't use Int as something I stack. However, I do suggest stacking Int if one is MT healing until their is balance between throughput and regen for the player. This is why a Disc MT healer should be stacking Int until they either (1) Are not running out of mana every fight or (2) realize their need for stronger heals.

Priests that are using 232 or lower gear will need the extra Int until they have that mana pool. In high end gear, I do agree that SP is the way to go once that mana pool works for that player.

I agree with the fact that if they're below 232 gear that they should be gemming int, seeing as they probably have less then a 24k or 25k mana pool. However, an undergeared Disc MT healer is not the best choice either. I wouldn't trying to MT heal if you're not already in 232+ gear, 245+ for 25 ICC (even though ICC is pretty much a joke for the easy modes) I'm sure that the healing will get more intense as new content is released. On the same note our gear will increase with the release too so still wont be that much of a difference imo.

I've noticed a lot of posts about disc etc, what do you think about Emp Renew? I used to think it was unuseful talent. That is until I respecced into it. I find emp renew spec doing very very well in 25 man raids. I know for our 25 togc anub as emp renew spec I destroy meters until P3 where the Holy paladins just Beacon and HL spam and inch me out in the end. But for a lot of encounters I've noticed that emp renew does very well, and I seem to be pretty mana effecient as well. Only when I have to ramp a serendipty and PoH spam do i see mana becoming an issue (I just HoH and fiend so its not that big of a deal)

Not all DKP systems are the same, so whether or not it's a smart purchase is difficult to answer without more information. It's a bit like saying, "Buy a car costs me money. Which car should I buy?" The answer depends heavily on the relative prices. Both trinkets are clear upgrades from the Pandora's Plea you are using now.

My intuition says that [Althor's Abacus] will beat the 245 Solace unless you are running out on mana, as it has way higher throughput. It's almost certainly the better long term option. As you get more gear upgrades, throughput matters more than mana longevity. But if your options are Solace for 5 points versus Abacus for 100, I'd take the Solace.

Dual Solace looks to me to be by far BiS, also in ICC. Though I can't find the quote now, [Althor's Abacus]'s proc seems relatively useless. It heals a random target, so most of the time it'll just overheal when you don't need it to. Even though it has more spellpower than Solace, Solace is still very over budgeted. Meaning if you have dual Solace, you can probably skip a lot of spirit/mp5 gear, thereby adding more haste/crit for more throughput. If you have any intellect gems at all right now, Solace seems like a no-brainer. Even [Purified Lunar Dust] seems better than [Althor's Abacus]. Same thing again, a little less spellpower, but lots of mp5.

It procced twice for me on Saurfang.

I'd say good pvp trinket, but I wouldn't take it over a Solace.

World of Logs - Real Time Raid Analysis

Name of the spell is Echoes of Light. It appears to be affected by some of my talents AND my crit rate. It was regularly critting for over 10k when I was Holy. I am not sure if this means it procs Divine Aegis as Discipline.

Points of interest: It likes to target Mirror Images, Shadowfiends, DK Ghouls, Shaman Elementals, Warlock Imps. Nice use of an ICD when that happens.

Don't discount the [Sliver of Pure Ice]. Especially when the heroic version of it will likely restore ~2000 mana every 2 minutes and probably near 200 spellpower.

The nice part about the clicky mana regen over the passive mana regen is you can use it when/if needed. Passive regen on trinkets is great but there are times where I find I just wish I could squeeze out another 'chunk' of mana.