I see this sentiment a lot here; something along the lines of "there's too much left to happen, and one book isn't enough to tell it."

Aside from the fallacy of incredulity here, I think that - on the contrary - there's plenty of time to finish the story.

There are two bits of reasoning here:

1. Plots tend to accelerate in the final third, as all the laying-the-groundwork has happened, and you can just get things done. (Examples: Scott Pilgrim vs The World (the film): 3/4 of the way into the film he's still got three evil exes to face. In The Princess Bride we're also about 2/3rds of the way through the film when Inigo still has to find the six fingered man, Westley still has to escape the pit of dispair AND find Buttercup AND rescue her AND be revived from the dead somehow AND Humperdink has to face his comuppance AND Rugen has to face his and ... it's all too much to fit into the final half-hour! Oh, wait...) See also The House of the Spirits (book, I've not seen the film), Stardust, any Sherlock Holmes story, and this is just stuff I have near enough to read the title.) I really believe that the third book could have Kote's narration done by the 1/3rd mark, and spend the rest of its time in the frame, with Kvothe and Bast and whatever allies they have trying to sort things out there. (Alternately, it could take the rest of the book, and at the end Kote has his story out, Bast understands why he wants to die and it finishes with Kote taking his life...either or.)

Secondly: The books are huge! Both of them are entire Lord of the Rings saga length books. Do people seriously think that a wordcount big enough Lord of the Rings is not long enough to tell us what happens? We're already at the precipice of disaster, and it just needs a nudge, and you really think it will take more than Lord of the Rings to tell us about that nudge? Really? "But he has to find the place and set up the inn." Not so hard: "With no options left to me, and no-one to turn to I changed my name and ran to the first village I found. I used some the money I had to buy a place and set up an inn, thinking of the innkeeper who was kind to me on my last day Tarbean. And that is where you find me now." Done.

I'm sure there's a lot more of the world to be seen after DoS, but there's really plenty of time to finish Kote's story.