What is the advantages and disadvantages of maintaining one ORACLE_HOME? I am a little confused about why a DBA would want to maintain one ORACLE_HOME? I can see no advantages.

Having multiple homes would allow multiple versions of Oracle installed.
First of all if you want to have multiple oracle version (11g, 12c etc.) you must have multiple homes.

The advantage of one oracle home is less space consumed. Less work with patching one home.

But if you have more instances under this one home, you have to patch all databases (post patch sql) which is more work :-).

So it depends on how many versions and how many instances do you have on the server.