Is cast speed a paper tiger?

I was swapping some things around with a build yesterday and came across an interesting thing. When I put on my Ingenuity which added 31% to both rings, and both rings having 8% mana and 240 mana, on a build that stacks mana for damage, my damage went down.

Now, the tool tip damage was higher with no belt at all. The only difference, the cast speed loss from the weight of the belt, vs no belt. There were some particular reasons why that was happening, but it highlighted the effect of cast speed on dps. The interesting thing was that all hits were higher with the belt on, but dps lower.

The only time that cast speed translates to real damage is when you are constantly casting, which is not that common. Even spark builds stop casting sometimes to move, etc.

My particular build uses entangle, CoC, and CoA. I barely cast more than once a second, so cast speed is almost irrelevant to actual damage output.

Maybe everyone knows this, but I see builds all the time with rapid casting in skills that don't need it or are not used in a way that it helps. Does it make the dps number higher, yes. Does it actually do more damage, usually no.