Increased Cooldown Recovery Speed (ICRS)

Evening dudes,

I have a few questions regarding (increased) cooldown recovery speed.

I'm playing a triggered assassin (5 triggered spells and a CoC) and I want to know at what points does the ICRS make a difference? (only in relation to spellslinger)

Spellslinger has a 500ms c/d.
Cast a socketed spell has a 4 second c/d.
CoC has a 150ms c/s.
Neither of these times take into account that the server has a tick rate and updates every 33ms(?).

Im currently running 30% helm enchant, 15% boots and I have just crafted an 11% belt. That's a total ICRS of 56%. From my research that means I should have an aps of 3.03 and a c/d of 330ms (this is persistent from 52%-69%). As far as I can see the belt makes absolutely no difference to the amount of spells being cast and my tooltip dps actually goes down. My aps without the belt is 2.75. How can casting the same spell more times per second mean less dps?

Finally, semi rant time, why does this not have any stat showing in the tool tip? What's the point in showing me casts per second when it is a triggered skill that I cannot cast?!? Why wouldn't that change to triggers per second? GGG know that we don't have access to the same external features that pc players have so I can't understand why they don't include basic things like relevant tool tips.