To put it another way, a high-temperature mad-libs machine will write a very unusual story, but that isn't necessarily the same as a clever story.

So why is this "temperature" not on, like, a rotary encoder?

So you can just, like, tweak it when it's working against your intent in either direction?

AFAIK there's no algorithmic reason against it, but services might not expose the controls in a convenient way, or at all.