Alright, here's my idea. Points as follows:
1. The Shardblades and Plate were originally the symbols of a Radiant's oath.
2. The glow that we see in Pre-Recreance Shards is a visible sign of Honor's favor, possibly indicating that he fuels the Plate/Radiant as much Light as needed without having to use gems.
3. At the Recreance, the Radiants broke their oaths.
4. This is why the Plate and Blades stopped glowing and now need gems. (Honor is no longer fueling them).
5. This is also why Syl hates the Sharblades (they are now symbols of broken oaths, exactly opposite her nature.)
6. If Kaladin ever gets ahold of Plate and Blade, they will presumably start glowing again (though maybe only once he's taken all five oaths)
7. What do you think?