"What the application does" may not be what you think of, as it is dependent on how secure the application or the layers beneath it are. This is how people get everything pwned step by step. The database server may then reveal credentials to other apps etc.
Sure. Defense in depth is important. But I hope that your application is only able to talk TCP/5432 to psql. No amount of psql upgrading will protect you against SQL injections in shitty application code.
Sure, but then chances are it's hosted on a nas with other data which you dont want ransomware'd, has access to other parts of the network, etc. - it's easy to underestimate the potential impact