Their very inclusion hurts the integrity of the story.
For instance, how could Delphine have correctly assumed that the Greybeards would send the LDB to Ustengrav?
In what manner did she obtain the Horn of JWC without using Whirlwind Sprint?
How is it that Delphine, having a keen mind and being well-travelled, could even suspect that the Thalmor are behind the return of the dragons? (And this is also considering that she was working with a scholar well-versed in Skyrim's history no less.)
Why would she put you directly in harm's way to infiltrate the Thalmor Embassy alone? What if we did not have the right skills? Can't she get into contact with someone more qualified for the task?
Did they purposefully make the Nords ignorant of their culture and history in order to give Esbern some value by being the only one who can remind us that Alduin is the Aurbis' Kalpa-reset machine?
The parts of the MQ which involve doing any sort of thing on their behalf are among the worst since I find myself asking questions that I really shouldn't. They feel extremely shoehorned-in.