As of the current game updates, Loyalty does NOT, in ANY WAY, give you any sort of strategic advantage. In fact, it doesn't give you any advantage at all whatsoever.
You can pay your Knights to have their loyalties increased, for varying amounts of Gold. It simply gives you the intangible benefit of them being happier about serving you.
It is believed that Loyalty is an intended feature for a future patch/game update, and will therefore reward players for taking advantage of this loyalty-boosting early. (AsheronRealaida being one of them.)
Otherwise, if this otherwise intangible feature was not intended for tangibility in a future patch, then there would be absolutely no point in making Loyalty a feature in Kingdoms of Camelot in the first place, now would there?