I used to use a similar system until I switched to a password manager. Convenience is a big factor, it’s nice to not have to think about logging in. Also coupled with that a secure password is a long password, so not having to type it in is a bonus.

The person says that, since the beginning of the password is unique, its “unhackable”, and that the attacker would need like 3 samples of the password to figure out their system.

I’ve had my data leaked more than 3 times, it’s not an unlikely scenario that someone could get a list of passwords used by someone.

Also once their system is compromised, they have to come up with a new system, then go and change every password. Which if it was me would be hundreds of places. With a password manager there’s no reason not to have completely unique passwords for everything, so if there is a leak, oh well, just change that password.