So a S8 SP with full Satin set, critical offparts, critical weapon and a critical trinket would have around 28% strike critical rating. The average S8 PvP player would have enough resilience to reduce the chance that they recieve a critical strike by approximitely 13%. Just by dividing we can see that you will have around 15% realistic chance to deal a critical strike. Critical talents are not even worth taking as you would sacrafice other more useful ones. So, is 15% critical chance really worth losing the majority of your mana regen and haste rating?
Yes, you will need the mana regen even if you have S8 gear. The Shadow Priest is not an Affliction Warlock. You are forced to healbot your partner very often. You have to dispel yourself, your partner and the enemies constantly. You have to pretty much shield yourself and your partner everytime possible. Critical would be a wasted stat by doing those (maybe except healing as heals can crit) while haste and mana regen would help greatly. Even as a "DPS" you would still be kind of a support class. You would be forced to stay outside of Shadowform very often aswell which would mean your dots wouldn't even be eligible to deal a critical strike.
Even when playing double DPS arenas can be pretty long. A good SP/Mage can survive vs DPS/Heal (especially if the Heal can't dispell - aka Shaman/Druid) team for eternity just by controling the DPS and kiting, for which you will need mana regen. Certain SP comps have to reset the fight a couple of times in order to kill a target (e.g. you burst Holy Paladin -> he trinkets so you have to reset, you burst him again -> he bubbles so you have to reset again, you burst a third time -> he has nothing and he dies), going all in wouldn't bring you a great success.
Nonetheless, if you want to deal more damage as SP, why gear up with critical strike from which half is gonna get negated by resilience and has no other use other than critting, when you can gear up with haste that is not only gonna make your global CD shorter (for all abilities, not only the offensive ones), your dots ticking faster, casting abilities faster (which again makes you deal more damag as crit would) and on top of that it has nothing to get countered with as critical does?
Fighting a DK is tricky. Bursting a DK as SP is not possible in general, I don't think that 15% extra critical strike chance is gonna help you. DKs will use all of their defensive cooldowns one after another which you pretty much have to sustain trough (you need mana to do it) and then kill them. Doesn't matter how much critical strike chance you got if he has an Anti-Magic Shell on.
Critical SP can work in duels against people with less resilience as duels truly don't last for long (unlike arenas), but it's again pretty RNG based as you might not get a single critical the whole duel so all the critical you have would be wasted, while if you had haste it would help you atleast slightly.
As for trinkets as a human, DFO and CTS can be used together in certain comps, for 5v5 or for duels but in other situations DFO + Solace or CTS + Solace would be better. I also like using [Bauble of True Blood] alot as it has saved me from sticky situations plenty of times.