Haven't talked to anyone who didn't think Delphine the Blade wasn't a snobbish bitch interested in only her goals.
"The Blades do not serve the Dragonborn and never have!"  quote from the Graybeards.

Well now you can silence her by killing her.  Care must be taken however.  Killing her too early can really mess up the story line and make many quests unavailable.  She can be killed by other npcs or animals as well so protect her on the road to kill the dragon.  A good Follower can be handy.
Npcs are never attacked on the road unless you are with them so you can leave them behind without fear of them being killed.

The biggest danger is at the SkyHaven Temple.  Don't let the bandits kill her.  Since I know its location I go there before beginning the quest and eliminate all the bandits.

After completing the SkyHaven Temple quest you can kill her whenever you like. Esburn doesn't seem to mind.
Caution!  If you plan on negotiating a truce so you can go kill Alduin I don't know what effect Delphine's absentness at the peace table will create.

I tested this mod on a new game and it works fine but it doesn't work on any of my old saved games.

Installation:  Unzip Delphine.zip into your Data folder of Skyrim or use MO.