I am quite new to this stuff so this question might be trivial. I was reading about bb84 and, as I understood it, after Alice sends $\psi$ Bob chooses a random sequence $b'$ and makes a measurement in either $X$ or $Z$ according to $b'$. After Bob does this he announces that he has received $\psi$ and both him and Alice compare the sequences $b$ and $b'$ discarding the terms for which $b \neq b'$.
What I don't understand: what would be the problem if, after Bob receives $\psi$, he simply announces this fact without choosing $b'$ and making measurements. In this case Alice communicates $b$ to Bob over a public channel and there are no bits to discard.
It seems that Alice has to communicate $b$ to Bob over a public channel in BB84, so why not do it after Bob claims to have received $\psi$?