Why can't exhaustive search parsing stop after |w| + 1 derivations? If my grammar does not have productions of the form $A\rightarrow\lambda$ and $A\rightarrow B$ for some variables $A$ and $B$ then I know that each step in the derivation must involve an increase in the sentential length. Therefore if I do an exhaustive search for some word $w$ then I know I can stop searching after $|w|$ derivations. 

My question is why then do textbooks assert that we can stop after $2|w|$ derivations instead? Yes, I agree that this is true, but wouldn't it be easier just to stop at $|w|+1$ and above? What am I missing for this condition?
You increase the length of the sequential form with each derivation, but you also need to convert non-terminals to terminals.

Think of a grammar in Chomsky normal form. For each word symbol, you need to create a non-terminal first (and you create only one per derivation!) and then convert it into a terminal. That's $2|w| \pm 1$ derivations right there. 

Yes, CNF is a little wasteful this way, but finding short derivations isn't its purpose, isn't it?