The only truly secure computer is one that is isolated from the internet, turned off, unplugged, buried in a bunker 100ft under ground, with armed guards at the only entrance. Even then, I'd check in on it every once in a while.
Hashing the passwords is part of what is known as "security in depth." You are correct that, in an ideal world, you would not make any mistakes which would give attackers access to that data, so in theory it would not matter if they were plaintext passwords or hashes. In a real world, intrusions do occur, and it remarkably hard to predict how and where they will occur. The idea behind security in depth is to make it so that, in theory, even if an attacker compromises your system in some way, you have taken efforts to mitigate the damage.
In the real world, there is a natural need to access hashes on a regular basis. Every time a user logs in, you need the ability to access them. Accordingly, they are almost always accessible to whatever application is doing the authentication. If someone compromises your application, they may be able to read data that they weren't supposed to be able to read.
The ways these attacks occur are endless. You can have SQL injection attacks if you failed to sanitize your inputs. You could have a buffer overrun, giving the attacker the ability to run their own code. You could have a permissions error, accidentally making a file readable by people when you shouldn't have. The attacker may get their hands on one of your backup tapes due to mishandling by your backup service!
All of these attacks give an attacker a foothold on your computer, but they don't always result in a complete break. You may have chrooted your SQL server, so that the SQL server process literally cannot see the entire rest of the computer. However, in such situations, the login information users need must be within the SQL server's reach, or its of no value. Thus, login information is typically compromised before other more nefarious compromises occur.
By hashing the passwords, you decrease their value. A hash isn't useful for login purposes. They need to have the password which hashes to that value. They may or may not be able to afford the cost of breaking the hash. In the best of all worlds, you never needed to worry about this in the first place, but if you subscribe to the security in depth approach, you make sure that even a successful intrusion doesn't compromise all of your data.