I've found this problem to be more evident with bivalves, but I have noticed it with shrimp dishes, as well. It has to do with the iodine levels in the shellfish, and it can be very obnoxious. Its the main reason that I almost always go with a rose when having a paella that has shellfish, even if there is game/fowl involved. The one red that I have had recently that did not exhibit this quality was a red Txacolina, but that was a red wine in color only - high acid and slightly spritzy, just like the whites from the region.
I do not like the Cone of Shame!