I have honestly not been keeping up with this thread, so I apologize if something I say has already been said or discussed.
Remember how the Knights Radiants' armor glowed and they were able to jump and fly in a similar manner to the way Szeth or Kaladin probably could if they got advanced enough and had enough Stormlight?
My theory is that eventually Syl will outgrow her body's capability to hold power. I think at this time she will become a Blade and/or Plate and perhaps change back to a Spren when she is not being used.
If you think about it, not everyone can see all Spren right? (e.g. You have to be drunk to see that one Spren.) Now perhaps all Blades are made this way. Where do they go when they disappear? I propose they turn back into Spren, but no one is attuned to them so no one sees them. Perhaps this is why Syl loathes the other Blades so much. They could be a different type of Spren, a corrupt, evil version of herself.
When someone intentionally puts a Blade down it doesn't evaporate. We know Spren can be caught and put into gems. This could be a similar concept.
If she turned into Plate, her abilities to Bind would still be usable by her, which could explain the Radiant's being able to do it even though they were in Plate.
This could also explain why Szeth wouldn't be able to use his Binding in another set of Plate, because it's from a different type of Spren and it doesn't interact with the Honor Spren.