Compared to password reuse, or using weak passwords, a password manager is better. Even if it's a long plaintext file in a dropbox.
Firstly. You know exactly which services you need to perform a password reset when they get stolen. In my case, all 357 of them.
Secondly, strong unique passwords prevents automated password stuffing, automated brute-force and hashing attacks, which is most of the attacks as I understand it.
Don't trust them, sure. Plan for them to be breached. But do use them. It's just better practice than the alternatives.