If the site has control over my money or my public persona, then I very much need to care how they handle my password.
It is not uncommon for databases to be stolen via lost laptops, human error, or sloppy security. When this happens, I would prefer that the database not contain my plaintext password.
If someone obtains my password through such a leak, it won't help me that I've used a distinct password for that website.
It's bad news when a bank leaks their customer list. It's catastrophic news when a bank leaks their customer passwords.
If you don't store the passwords in the first place, they can't be leaked.
It is not uncommon for databases to be stolen via lost laptops, human error, or sloppy security. When this happens, I would prefer that the database not contain my plaintext password.
If someone obtains my password through such a leak, it won't help me that I've used a distinct password for that website.
It's bad news when a bank leaks their customer list. It's catastrophic news when a bank leaks their customer passwords.
If you don't store the passwords in the first place, they can't be leaked.