I use dry parsley, cilantro, and other herbs, but I almost never use the fresh stuff. What’s the difference? The leaves are 1) washed thoroughly and 2) chopped up and dried. So if there were any bugs, it’s a safek if they were still there after washing. It’s a safek if any remianing bugs are whole anymore. And once dried, they crumble and disintegrate. That becomes a s’fek sefaika.
I imagine that freezing facilitates the breaking into pieces any possible bugs left over from a cleansing. Just my guess.