I would guess that something different is happening with Shardplate. Seeing as Shardplate doesn't cause the screaming that Shardblades cause when a Radiant touches it I'm not sure we can jump to the conclusion that Plate is also from dead Spren. In addition, we don't see nearly the animosity from Syl, the Stormfather, etc. regarding Shardplate as they have toward Dead Spren blades.
Something else to consider; Sprenblades were the result of the Spren trying to copy the Honorblades, we don't have any indication that the Heralds wore Shardplate, what then would the Spren be copying?