1) What's the point of Ecclesitheurge then, if not to be able to cast non-Cleric spells? Access to a few cute domain spells and a small buff that requires a standard action and only lasts a turn unless you burn heals? In exchange for losing armor and Cleric weapons?
2) An Arcane Trickster doesn't have the ability to heal up your entire party after the fight. That's the point of Eccle - you get the offensive casting of a Wizard, with the crazy Channel healing that a Cleric gets. And you don't need fucking Selective Channel and Extra Channel to do that. Healing during fights is inefficient, but if it's really necessary the Cleric already has tools to do that in the shape of spontaneous casting, he doesn't need to burn feats to do it via Channel.
3) You can still dip to get stat boosts if you want. How does me giving Tristian a different domain stop you from a Cognatogen dip?
4) The way I've modified Tristian, you can still cast Archon's Aura... in fact, he's even better at it than he was before. This criticism makes zero sense. Archon's takes one action to cast, and you can even cast it just before a fight once you get high level enough. So it's not Archon's OR Fireballs, you can do both.
(1) In PnP it's probably a little more straightforward. You're intended to use your Blessing as your default action economy when not casting big spells. +2 Sacred (stacks with everything) to attacks/saves/AC turns out to be pretty freaking solid if applied strategically. The +2 is relatively less impressive given the higher stats in P:K, but it's still the equivalent of a Mutagen boost +3 on Saves. The Long version lasts throughout a battle by midgame, and you spend your Channels on it, making Extra Channel a better feat for Ecclesi than any other class.
The Domain spells are better than cute since you end up with clunker levels in all Domains, making choosing from five options both more likely to be good and more flexible. Also flexible: as a 3/4 class that gets fast progression to Divine Power, Eaglesoul, and Frightful Aspect you can also pivot into a very solid big Haplo bopper if the right weapon shows up from the artisans, as happened in this playthrough with Serpent Prince. Starting with Extend Metamagic helps a lot with those shorter duration self-buffs.
2) There's already more than enough options for after fight healing, starting with a bazillion healing potions. Bards can heal by lvl 12. After fight healing is Cleric benefit number 4 or 5 in importance. Given Tristian's extra Channels (main use are for Long Blessings and frying Undead), it gives you a lot of resilience being able to fire one off mid-combat, so Selective Channeling is a solid choice for him where it wouldn't be for Harrim. The Spell Focus feats are extraordinarily weak - you can get a Rod that gives +3 DC and one of the benefits of nukes in the first place is that they don't absolutely have to beat saves every time to have a good effect.
3) Every level you splash hurts Spell Pen, Caster lvl, Domain abilities (Touch of Good obv, but so nice to have an always on Rez like high level Rebuke Death can be, and Holy Lance starts showing up vs. Devourers), casts, durations, BAB, what have you. Really think hard about opportunity costs.
4) They take up the same slots, although with Tristian's original build you can shift Aura to lvl 4 with Extend Metamagic, which is a good idea. There are still better Cleric spells at that level like Animate Dead and Magical Vestment, not to mention Delay Poison and Resist Energy.