Why can't exhaustive search parsing stop after |w| + 1 derivations?
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?