When considering the wars going on, and threat of the Thalmor, supporting and helping rebuild the Blades might be better than keeping the Greybeards happy. After the MQ the Greybeards go back to being useless and not caring about what goes on in the world below, they don't care who wins the civil war, nor do they seem to care about the Thalmor threat. The Blades on the other hand are mortal enemies of the Thalmor, and rebuilding the Blades can only help in defeating the Thalmor. Also I am not entirely convinced that Paarthurnax is truly 100% reformed, When confronted about the Blades desire to have him killed, Paarthurnax tells you that he is reformed now, but in the same conversation he says that dominating others is the nature of dragons, and that not a day goes by where he is not tempted to return to his old ways. Only through self control and mediation is Paarthurnax able to resist those urges, so what's to say in the future he will never lose control? Specially now that Alduin is out of the picture, and Paarthurnax has taken his place as the eldest dragon.
You don't need to be 100% convinced, it technically shouldn't be that simple, as good character development doesn't make perfect characters. And because your a dragonborn you have the same desires as well the Blades should just give you a quest to kill yourself just in case you get out of hand. (following the Blades logic puts your hero on a http://tvtropes.org/pmwiki/pmwiki.php/Main/JumpingOffTheSlipperySlope condition)
It is quite simple from a story RP standpoint you kill an atoner who just helped prevent genocide twice in countless years or side with a two buggy and illogical characters. (Which has greater impact saving the world or participating in another war) Stopping the civil war would literally involve them taking over Skyrim in terms of power which is exactly opposite to why the graybeards are so respected by both sides. Paarthurnax gave humans their freedom back so jumping in and sorting everything out for them would infringe on that freedom.
The blades are replaceable in their current state as they don't actually exist as an organization so are functionally useless in the grand scheme of things. At least Paarthurnax is going to try to teach the other dragons the way of the voice it's something you might hope would help in the future. If he ever does do a face heel turn then it isn't like he is special in any way like Alduin. (Their "mortal enemies" of logic in reality as they let their dynamic oath get in the way of actually thinking things through properly)
The dialog they use is particularly telling as well (http://i67.photobucket.com/albums/h297/Heresiarchqin/4.jpg) which makes them seem awfully like they are literally saying the to them he has http://tvtropes.org/pmwiki/pmwiki.php/Main/YouHaveOutlivedYourUsefulness (Which is not normal)