I'm kinda fond of Esbern, because he's got that whole absent-minded professor thing going and would probably be a source of endless fascinating information if you got the chance to sit down and talk to him for a good long while. And while I disagree with their stance on Paarthurnax, he makes a better argument for their side because at least he seems rational and somewhat thoughtful about it.
Delphine, on the other hand, is just so hateful and contemptuous towards anyone awho isn't doing what she wants them to do, because she thinks HER way is the only right way and if you don't agree then she has no use for you whatsoever. What is it that makes her so impossibly certain that she's right about anything and everything? Her gut? The same gut that told you the Thalmor were absolutely for sure the ones behind the return of the dragons? Thanks, but no thanks.
I use the Paarthurnax Dilemma mod which lets me refuse to kill Paarthy and then tell the Blades exactly what to do with their ultimatum about it. Pretty sure that after that they are all nice and cosy with the Dragonborn again, but even so I still have no use for them... just like they had no use for me when I stopped asking "how high" every time Delphine told me to jump. They only things they can do at that point, I don't need from them. I can find and kill dragons all by myself, if that's what I want to do, without their guidance or assistance.
And I don't help rebuild them because I don't want people who are my friends or in my service to be subject to Delphine's BS, or to have to choose between me and their oath to the faction. If Delphine wants new recruits then she and her all-knowing gut can go out and find them instead of sitting around in the new digs I provided for them and doing nothing all day long.
Ideally my Dragonborn would be able to bring Esbern around completely on the Paarthurnax issue through conversation and persuasion, and arrange for the two of them to meet and become friends if possible. Considering that Esbern is a historian and particularly devoted to the history of dragons in Tamriel, for him it would be a gold mine. And for Paarthurnax, he'd finally have someone who was willing to climb that mountain every now and then just for some tinvaak with an old dovah.