As I've said, it's a reasonable request. Keyword being request.
I understand that he used to be a bad guy, and they want him to answer for his crimes. Given everything I do for them, though... delve into a dangerous Draugr temple for a stone tablet that might not've existed (don't forget that it was Delphine that wanted that; Farengar was just the means to get me to do it), infiltrate an "enemy" base for information she was looking for, find Esbern whom she thought was long dead, open my home to them, be willing to rebuild the Blades, kill a crapton of dragons, save the world... if they can't heed my guidance that Paarthurnax doesn't deserve to die because of how helpful he has been and will be, then I'm sorry, to still demand his head stops being reasonable.
Makes sense.
But then, again, all that stuff you listed (with the exception of helping to rebuild the Blades of course), is not stuff you're doing FOR the Blades, it's stuff you're doing because it furthers the whole 'stop the world from ending' agenda. It's not like you're doing them personal favors there; they gain from your actions, this is entirely true, but mostly out of happy accident, and at the same time they're also repeatedly risking their necks for the same reasons. While you get many of your early 'go here, do this' things from the Blades, that's because they're working with you in trying to figure things out, and not because Delphine has any idea that asking a court mage to find someone to go find a dragon stone in an old ruin is going to lead to finding Esbern still alive and reopening an old Blades temple that I don't think she even knew existed.
I don't think the risk they're taking can be overstated: you're the Dragonborn, blessed with some pretty crazy powers that most people will never come close to, and by the time of the end of the main quest, people know who and what you are and you get praised by random guards on the street (when they aren't sneering about sweetrolls), and you're almost certainly Thane of the richest and one of the most influential holds in Skyrim. The Thalmor can't openly act against you (not that this stops their random patrols or the occasional hit squad, of course), even when you toss their ambassador out of the peace conference on her snotty elven bum, but the Blades enjoy no such protections. The entire reason they come out of hiding is to try and help with the dragon situation, and even after you've told them what they can go do with themselves for wanting you to kill Paarthurnax, they'll show up at the peace conference to argue for your cause and provide you with the one thing you're lacking (the ability to actually call a dragon to your trap in Whiterun).
You know what they could have done if they really wanted to be shortsighted, grudge-holding [censored]s? ...They could have shown up at the peace conference and gone, 'You shouldn't listen to this person, because as much as he/she claims to be fighting for the good of the world, he/she is friends with Alduin's former second-in-command. Oh, and these Greycloaks that you revere, and who are the reason you accepted this place for your conference? They've been hiding that dragon on the top of their mountain this entire time. He's their teacher! This is all a ploy to get you to lower your guards' etc etc. They could have singlehandledly sabotaged the entire thing, and given how touch and go that entire meeting was, I'm not sure they wouldn't have been successful. Instead they basically tell Ulfric and Tullius to sit down, shut up, and stop getting in the way of saving the world.