I find the resolution without killing Paarthu quite intriguing: Dragons are back in Tamriel - good for any fantasy setting - there are decent ones following the way of the voice, and there are nasty ones searching for a return to the ways of old when dragons ruled over humans. The Blades as a group of zealous Dragonslayers akin to the Vigilants of Stendarr sure have a place in that world, but they have outlived their purpose as "protector" of the Dragonborn. The Dovahkiin doesn't need their protection, and it is no longer necessary that the emperor of Tamriel is a Dragonborn. And without a grand purpose, the Blades will be forgotten by history.
Well, like you said, it's intriguing. But it isn't resolved. There's a helluva lot more story potential there. Are you saying you don't want to hear about/play through it? That your mind is already made up about everything and to just move on?
As for the Blades, well.. it goes back to my Bourne comparison. They still may have a purpose with the dragonborn. Or might reach out. Or they might even be capable of things that softens the relationship with the player. It doesn't mean that you'd need to be on their side, but I could see a sort of shaky alliance happening with them possibly. The same way her character was with Bourne. She works for a side that he doesn't trust, but he doesn't outright kill them either.
I think you're' jumping the gun though as far as "forgotten in history" goes. Bethesda hasn't even touched on Akavir settings yet, and you already want to wipe out the Blades. Who knows, maybe they will be forgotten in time.. but that would crap if it's handled in this way. If this was a novel, and you got rid of a longrunning faction in your series with a little footnote, I'd think it was laziest writing ever. There are way more interesting ways of extinguishing the Blades.