Science

Think of it in other terms.

Minkowsky space is basically information space. You can't get information about things that are farther away than lightspeed would allow data transmission. Outside of that "light cone" it's all unknowable, not just unknown. This keeps getting proven right, and Minkowsky's word preceded and enabled Einstein's.

But if gravity moved faster than light-speed, then if the Sun vanished and we knew that gravity "failed" before the last of the Sun's light reached us, we'd know the Sun was gone before we could know the Sun was gone. All sorts of implications from what we know about Minkowsky space and general relativity fail and we're in duck soup.