You are correct but are missing the forest for the trees as they say.

The original mutation is random, benefiting (or at least not harming) is selected for. So without the random mutation there isn't anything being selected for.

For example, say we need to change gene 1 from A to C for the fever to last 1 hour longer (this is very simplified of course) but throughout history no one has changed gene 1 to C then there will be no longer fever to select for.

We can't see evolution as something that moves creatures along with intent. Nothing is guaranteed since you must first have a random mutation to progress.