Channeled abilities cost at "tick" intervals which is tied to your Attack Speed so those builds suffer at high IAS% as it drains faster than they can sustain.
Arcane Power on Crit works at whatever the proc coefficient is for the skill so how well it'll generate your resource varies from skill to skill.
Sorry for taking so long to respond but I've been in meetings all day. As for your thoughts...
I see. That makes sense. But if I understand correctly, even though those channeling abilities are draining resource faster it's also doing higher damage during that second and tick. So it's not that you're failing to get a poor return or dealing less damage, right?
Since the 2.0.1 update and changes, APS is used as a damage multiplier for channeling abilities. Damage is APS*tooltip_damage/5 per frame (5 times per second).
So for example, if I'm using Disintegrate, have 2.00 APS and have 0 CC I might run out twice as fast as if I had the same weapon but removed all AS from my build...but I would have done twice as much damage, right?
If your only goal is spell channeling, it certainly defeats the purpose of simple resource/second regen during the channeling process, but unless you're doing a lot of "fail casting" (that is wasting your channeling time by mis-clicking targets or some such) you're getting all the damage you should be getting out of your resource. That is, there are no diminishing returns secondary to higher APS. But with higher APS, you have to make sure that you're hitting your targets because your channels are more "concentrated" and resource-draining, if you will.
I'm not entirely clear, but I know this is in the ballpark.
Well for DH if you're spamming a hatred spender, the faster you spam it the quicker you run out of hatred = bad. So replacing IAS with some other +dps affix is better. Your sheet damage may look even, but you keep your hatred from hitting 0 longer.
I'm still not totally clear on this example.
Let's say your resource spender for DH was Elemental Arrow or Rapid Fire. In one build you have 1.10 APS (assume 2H Crossbow) and in another 2.20AS (assume dual 1H Crossbows). In the later, you burn through your Hate faster because you're getting off twice as many attacks. Assuming you land all of them on target and that your damage is the same for both setups, you should be doing 2x the damage with the APS version in a given amount of time, but running out of Hate 2x as fast, right? That doesn't seem like a drawback; rather an acknowledgement that if your goal is to get off as many resource-spending attacks as you can in as short amount of time as possible, AS is the way to do that. If you can't stand still and channel something like Rapid Fire for an extended duration of time or if you don't have the finger/wrist speed to attack-move cast Elemental Arrow, you're losing because you're not getting much damage out per second. With APS, if you're not constantly attacking, you're losing. In which case you are indeed better with a slower, high-damage weapon.
And keep in mind, with high APS, you can regenerate your resource with source generating primaries really quickly too. 4 or 5 seconds and you're right back to channeling from max resource. Seems more like a playstyle issue rather than a "better" or "worse" issue, no?
I still may be missing something important.
For reference sake, I'm using this as my resource:
https://us.battle.net/d3/en/forum/topic/8770117237#1
It seems quite convoluted and I still may be missing some details. I did learn quite a bit from that page, though.