I think the main reason for SHA-256 a password is quite simple. You dont want to know the password. If you know the password you need to take some extra precautions in order to protect it propperly. Since a breach could expose the password it would lead to possible other attacks.
Also usually the software does not use the password itself to generate the hash, but some random junk is usually added to it to ensure that 2 users who picked "Pa55w0rd" dont show up with the same hash.
This added salt makes it very hard for the attacker to guess the password, even if he has access to the final hash. There are precomputed resuilts for simple SHA-256 operations out there, and they cover a great deal of the normal key space already (Called rainbow tables) These could be used to find a password related to an account. But these tables fail badly if you add a few bytes of random junk in fromt of the password, and they are even less usefull is each user has its own "random junk"
The only "drawback" is that you cant recover your password, and only reset it. (I hate online services that can send me my password since it shows they dont care)
As others mentioned this results in a convinient 256bit blob of data, which could be used as an 256 AES key. It also means that a password reset would invalidate all encrypted data (Which you might want depending on the data)