This process is something that I have inherited and it seems an unnecessary process, or am I missing something?
You are correct I do not see any sense in this process. For SP upgrade backup whole system and user databases, store it properly and then do upgrade. Also it goes without saying that you first test SP/CU on your test machine and then move the patch upgrade to prod.
For SP upgarde refer below
How-to-install-sql-server-2012-sp2-on-standalone-sql-server-instance.aspx