Weak passwords are still weak, but things like bcrypt buy you time. A bcrypt configuration might have hashing take 250ms on a server's Xeon CPU (as opposed to nanoseconds with a sha-based hash). You can try the password 'password' on say 50k hashes that were dumped, but it will take about 3.5 hours. You can get this time down by parallelizing or with better hardware like GPUs / FPGAs / ASICs, but you're still looking at a base time of 3.5 hours per attempt to go through each account. Or if you're only targeting one account, 3.5 hours to try 50k words.

If the server had bcrypt configured to take a second per password, multiple everything by 4. And so on. What I think is needed as a supplement to "use bcrypt / scrypt" is a "and use it this way so you don't accidentally open your server to DoSing or give a poor experience", because a 10 seconds-to-compute-on-a-Xeon hash is great from a security standpoint if your hashes get leaked, it sucks from a user experience to have to wait at least 10 seconds to login, and if you have to service multiple logins at once your server's not going to be able to do anything else if you just use bcrypt/scrypt synchronously.