The standard password manager is slightly better because the password database works like a 2nd factor.
Also, a character has at most 8 bits of entropy, not 64. If you use base 64 its only 6 bits of entropy. 16 x 6 = 96 bits is still more than enough though.
A downside if everyone used this scheme would be parallelized attacks on reversing the hash for the key. If you find a key that, with this scheme, creates a password for your service, you found the corresponding secret key. This then compromises all of that users passwords.
Sorry early morning here, I actually fixed that before I saw your comment -- more like 6 bits per character. In any case more than good enough.
I actually am not a fan of 2nd-factor authentication (e.g. phone). If you lose the physical thing or it gets leaked to a stranger, gunman who mugs you, leaked by security holes in the thing's own embedded OS, it's no longer helping your security. I'd rather authentication depend on only what's in my mind and body and nothing external. Also, I lose stuff and forget stuff pretty easily, so I often just avoid carrying anything.
Also, a character has at most 8 bits of entropy, not 64. If you use base 64 its only 6 bits of entropy. 16 x 6 = 96 bits is still more than enough though.
A downside if everyone used this scheme would be parallelized attacks on reversing the hash for the key. If you find a key that, with this scheme, creates a password for your service, you found the corresponding secret key. This then compromises all of that users passwords.