That's incorrect. It is a consequence of relativity.
and it also seems to be grossly out of touch with reality and emperical science.
There is not a single experimental result that contradicts relativity. This idea of "gravity propagating faster than gravitational waves" is a null concept, with no basis other than a trivial misunderstanding of what a field is. It's like saying that while you may walk at a finite speed, the ground beneath your feet is infinitely fast.
Something has to be wrong with the picture.
In other words, you don't like it. The universe is the way it is, and not how you would wish it to be.
No, it is not a null concept, and no, it is not like saying that the ground moves infinitely fast, as the latter analogy crucifies the distinction being made between a field covering an area that it did not cover from that of the ground already covering an area.
When you turn an electromagnet to the ON position, a magnetic field suddenly covers a new area that in the past it did not cover (as in, when the switch was OFF).
It is *valid* to inquire as to how fast that field covered the new area.
But it has not been proven to be valid to claim that the field will cover a new area at the same speed as *disturbances* to an already *existing* field propagate (which we are all in agreement that it happens at Light speed).
What we currently know is that an existing field will propagate changes at Light speed. Fine.
But not all electromagnets have been turned ON yet, so not all fields exist yet.
When turned ON, the magnetic field goes from covering ZERO area to covering some sizeable finite area.
Does that happen at the speed of Light? Well, it hasn't been conclusively shown to be that slow, yet.