I'm all for the Empire, but the Blades really have nothing to do with the Empire anymore. Once they were a great group, but then the Thalmor broke them and the Empire turned it's back on them. Now it's a few stragglers that are so narrowmindedly focused on killing dragons that it's all they really care about. They don't serve the Empire anymore and they certainly don't serve the Dragonborn. In fact, I'd go so far as to say that they want YOU to serve them.
I see them not quite as stereotyped as you do. Yes, they are tough and dominant and demanding, but I allow them to be it, because they have a "can do" attitude. While the Greybeards send me to get the
Horn of Jurgen Windcaller do the Blades got it all by themselves, and left a note, too!
The Greybeards only ever question my motive, they treat me like a dumb child and keep Paarthurnax secret from me while I carry their food up the hill. The Greybeards think that I should not know everything and the things they do let me know depend entirely on their will and whenever they think the time is right. Say, what do you make of that?
I have no desire to kill the Greybeards. I simply walk away from them and let them live in the stupid cold of the mountain. Maybe they are all wise, but they hide it well.
The Blades then offered all the information to me they had at the time. They gave me a map of all the dragon burial sites, they gave me the horn of jurgen windcaller, they help me to get into the Thalmor embassy, they trust me to recruit their new members, they train them and sent these new Blades to support me and they constantly find new dragons as well as offer a blessing.
I did hesitate when they asked me to kill Paarthurnax, but not because I have feelings for a dragon, but because I see Paarthurnax as a tool in my fight against the dragons. I could have cared less about justice and over one dragon at that time, but it was important to the Blades and I see them as my team. And in a team it is all for one and one for all.