[Disclosure: I work for AgileBits, the makers of 1Password]
As has been pointed out nicely by others, password managers are subject to different risks. I obviously feel that using a well designed password manager is a good choice.
I want to address the "eggs in one basket" issue that has been raised. Yes, password managers do put all of your eggs in one basket, and so you should look at how well that basket is protected. But let's look at the same security issue (many eggs in a basket) when not using a password manager.
Password reuse is also putting multiple eggs in a basket
Suppose that Molly (one of my dogs) reuses the the password
1chaseR4bbits for ten different sites and services. (Molly is not a very bright dog.) By doing so each of those ten sites becomes an egg in the same basket. If her password is discovered, all of her accounts on those sites are compromised.
Now let's look at how well that reuse basket is protected. It is vulnerable to her password being captured in transit, it is vulnerable to phishing, it is vulnerable to a breach of any one of the ten sites and services. Indeed, the bigger the basket (the more sites she reuses the password on) the more vulnerable it is.
Quite simply, password reuse is putting multiple eggs in one very poorly protected basket. A good password manager solves the password reuse problem, and gives you a very solid basket.
You listed phishing attacks as a threat to ones Master Password for a password manager. With 1Password, the app runs completely locally, so there is little scope for a phishing attack. There is potentially scope for some locally running program to try to spoof 1Password. We haven't seen anything like that (yet) and so have not enabled counter measures. (Anyone remember site-keys? Yuck!)
You mentioned the difficulty of maintaining even a small number of strong, memorable, type-able passwords. About four years ago, I wrote up advice (see Towards Better Master Passwords) on how to do this for the few passwords you do need to remember. It is advice which still holds today (and was picked up by XKCD) and if followed properly remains strong even if attackers know exactly what system you used.