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Even with an internal cooldown you still get more procs over time with haste.
The way to calculate the procs per timeframe with an item that has a cooldown (T) and an procs per time (A) before taking cooldown into account:
procs over time = 1 / (1/A + T)
This is pretty basic statistics relying on very little rounding.
of course the time units have to match (as in, if A is procs per second T must also be in seconds and the procs over time will give procs per second).
Of course this formula shows that anything that increases procs over time before taking cooldown into account has quite low effect on the final procs over time compared to the increase in final procs over time on items without internal cooldown when the basic procs over time is increased.
Taking into account overlapping procs also makes some difference, although probably much smaller than the cooldown effect, and definitely a LOT harder to calculate, since procs with cooldowns will never overlap with any items I know in game.
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