My problem of 4 years of algorithm use was that it would slowly change over time. I began to add mechanisms to predictably rotate the passwords. I began to add mechanisms that dealt with arcane dumb password requirements. Encountering a login from 3 years ago usually had me trying 3 different variants before getting it.
Furthermore, my algorithm still produces passwords that have considerably less entropy than a password generator will do for you.
The other advantage of password managers are for those damn security questions. I now routinely use 4-word diceware generated password as my security question answers and can store those in 1Password as well. The number of websites that let you bypass login with just a security question is mind blowing.