If there is no speed limit on space-time compression, why do gravitational waves travel at light-speed? From what I've read about spacetime and general relativity it seems there is no limit on how quickly space-time can be compressed or expanded. Why then gravitational waves are limited to light speed?
[Edit: I removed references to the Alcubierre metric since they are not relevant to the question]
 A: Firstly, gravitational waves travel at speed $c$ locally, so to someone inside a warp bubble, a gravitational wave also inside the bubble still keeps pace with light that is also inside the bubble.
Secondly, gravitational waves (like electromagnetic waves) only travel at speed $c$ in a vacuum. And you can't make a warp bubble out of vacuum spacetime. You need exotic matter in places, which makes it not a vacuum in those places.
A: There is no such thing as a limiting speed c for gravitational waves!
With this question, you have hit on an important topic that is usually badly discussed in lectures, articles and books.
There is no general law that says that the velocity of gravitational waves and gravitational perturbations is necessarily c. Nor is there any law that says that they cannot exceed the limit c. Yet they are almost always quoted as if they were proven theorems!
The misinterpretation originates from the fact that Einstein derived the speed c for a special type of gravitational waves - by the so-called linearized Einstein equations. So it is a special approximation when the spacetime over which the waves propagate can be taken as Minkowski spacetime and the intensity of the waves is weak. Clearly this is an important but very special type of all gravitational waves and effects.
It has been 100 years since then, and no one has been able to produce a similar derivation for all gravitational wave and effect propagation cases. But many researcher have tried many times... For some other special spacetimes there are similar approximate results.
But the question of the velocity of propagation of weak and strong gravitational waves and perturbations of curved spacetimes remains open, despite the false myth.
In fact, in advanced research that attempts to describe gravitational effects propagating in curved spacetimes ( coupled to material fields), it is usually concluded that the waves propagate at a speed other than c! They do not have a uniform velocity, but have a wide range of velocities depending on the couplings, the parameters and the way the approximation is made. They can propagate at speeds less than c, but also at speeds greater than c. This is all the best theoretical models can tell us for now. See for example this source, I highlight one statement in the abstract:
"We show that for the choice of interaction signs implied by S-matrix and spectral density positivity bounds suggested by analyticity and causality, the speed of gravitational waves is in general superluminal at
low-energies on NEC preserving backgrounds, meaning gravitational waves travel faster than allowedby the metric to which photons and Standard Model fields are minimally coupled. "- The Speed of Gravity
