yes, they do. password managers eliminate the need to memorize most passwords altogether and also make them unbreakable. a truly random password of length 16 consisting just of lower case letters has more than 2^64 combinations. no computer will ever bruteforce that.
making long hard to crack but easy to remember passwords using pass phrases as you suggest is ok for one or two main passwords but is a hopelessly bad strategy for managing all your passwords.
Most people have way too many important passwords that should be unique for that to work: several bank and credit card passwords, several email account passwords, several utilities passwords (cable, heating etc), insurance, social networks (twitter, facebook and so on), online shopping (ebay, amazon, paypal), travel sites (travelocity, expedia).
This is 20+ passwords minimum. for most people it's 30+. No regular person can memorize so many different passwords even if they are all pass phrases. so if you are not using a password manager you inevitably end up using the same password for multiple sites which is a really bad idea for sites that I listed which all have access to a lot of your financial and personal info.
That's why you keep 3-5 passphrases. One for social, one for forums, one for banking, and one for shopping.
ThisLittleBirdieWentToTarget
ThisGuyStoleMyVisaCard
This makes it easy to differentiate between shopping and banking.
The password managers are only as good as their ability to be updated and available. If my iPhone breaks, and I need to log into my account to transfer money because I'm stuck somewhere, I'm SOL. Why? Because my banking password was in 1Password and my email account to reset my password is also in 1Password. And since my iPhone broke, I can't even use 2-factor auth.
So tell me again, how are password managers better?