CorrectHorseBatteryStaple will fail for a lot of sites. It doesn't have special characters, it's too long, it doesn't have numbers, it contains dictionary words, etc.
And you still have to remember the unique phrase you chose for each site. If you have a couple dozen logins, can you remember 24 different phrases? What about when a site forces you to change your password?
A password manager. A much as I like CorrectHorseBatteryStaple, it would be impossible to use on every account I have (hundreds). I use CHBS for the few (5 at most) accounts that I log into all day, every day. Everything else gets a long, random string of garbage and stored in my password manager.
LastPass, unless you're able to memorize 200 different unique, complex passwords. Using a password "scheme" per site (like CorrectHorseBatteryStapleHN, CorrectHorseBatteryStapleReddit) is not safe.
This happened to me: I forgot a password (site was ThompsonReuters, so not a tiny company we-dont-know-better), and requested a restore via email. The mailed me the password in plain text: "Your password is CorrectHorseBatteryStaple, you can change it at url.com/change".
So imagine you use CorrectHorse, and some site stores passwords in plain text or weakly hashed, and then the DB is compromised (if they do badly the storage, chances are the DB is also weak), and boom, a cracker has your email, password, and the name of your first pet.
But if I use KeepPass, I don't care if my password leaks from that site or the other, or if they store in plain text. That password is only used in one site.
I use the CorrectHorseBatteryStaple format, but with a short string of digits/symbols at the end to satisfy picky rules. This generally seems to work. But since I use a different password for every website I don't see how I could not use a password manager of some sort ... making passwords easier to type and remember doesn't mean I'm going to remember them all.