In Skyrim, the Blades are one of the only stupid things I hate about the game. Sure, their goals seem to be to protect ALL of Tamriel...but they are doing nothing but hindering it by not aiding the Dragonborn should he/she refuse to kill Paarthurnax.
Here's some points I'm trying to get to; the way they function makes absolutely NO sense:
1. Delphine is set upon hindering any ties she has with the Dragonborn just at the thought that they will not kill Paarthurnax...she seems to possess some undying hatred of dragons. Why is that? Of course I know that the majority of dragons will do nothing but prey upon mortals they come across...but it's not like the dragons killed ANYONE close to Delphine, it wasn't the dragons who murdered her comrades during the Great War. She's acted like she's hated dragons her whole entire life...when they only started reappearing in weeks to a month before the defeat of Alduin. Really it makes way more sense if she were to focus her anger purely on the Thalmor...especially true since the defeat of Alduin and the dragons not being as much of a threat due to his leadership being lost and many of them being taught the Way of the Voice by joining Paarthurnax.
2. Esbern states that both the Greybeards and the Emperors (from both the Reman and Septim Empires) protected Paarthurnax. That would tell you the Emperors ordered the Blades to leave him alone. They swore loyalty to the Emperor (who was a Dragonborn) and so they were oath-bound to obey. Now they see that the Dragonborn is here again...only this time he/she does not hold a position of authority (Emperor/King, etc.) so they take advantage of this fact to push around the Dragonborn to do their will in order to please them. Even worse...they are showing no respect for the former Emperors who ordered them to leave Paarthurnax alone. If they had any respect for the Emperors...they'd carry out their Emperor's will even long after they died. But no...Delphine and Esbern are raising their middle fingers against the Great Dragonborn Emperors they once revered and protected...and are doing according to THEIR desires.
3. As said later in point 1, the Blades continue to focus on the dragons even after they become less of a threat after the defeat of Alduin and many join Paarthurnax on the Throat of the World to learn the Way of the Voice. They've completely forgotten that the Thalmor are still around....so they have bigger fish to fry.
4. Delphine criticizes the Greybeards for not doing anything about the Civil War in Skyrim. But here's a question I'd like to ask her: "What have YOU done about the war?" She could've done something about the war as well, she could've joined one of the sides (the Empire or the Stormcloaks) in the war and become an officer on either side with her combat experience as a Blade. Or they ( in the case that Delphine rebuilds the Blades) could've taken a different approach (referring to point 3) by helping both sides by fighting the Thalmor secretly (quite possible with the Thalmor distracted by constantly trying to keep the war raging to have better hold upon Skyrim). But no, they continue to dwell upon the dragons even when they are not as mush of a threat. The only thing the Blades even do in the war is during the Peace Council in "Season Unending" where they convince the sides to negotiate...but that's when the dragons were a threat since Alduin was on the loose. Now that the Dragon Crisis is over...they should focus on actually helping Skyrim and not focus as much on the dragons (this includes leaving Paarthurnax alone).
The Blades simply anger me with their arrogance, selfishness and irresponsibility. I think the Blades in this game are nothing but a nuisance.