You can transmit data by modulating in on top of something that propagates through space? Well, big deal, who'd thought? /s
In all seriousness, the big problem is, how to create gravitational waves in a controlled manner in the first place. Because the fact remains, that gravity is, by several orders of magnitude, the weakest force in our universe and it takes stooopid amounts of energy (and I means that in an all-encompassing way, referring to anything that goes into the metric tensor) to create an even noticeable ripple in spacetime. If we break down spectrally, its easiest to detect stuff close to DC, I mean, people did it 200 years ago, so to speak, but only over short distances, and really long integration times (https://en.wikipedia.org/wiki/Cavendish_experiment).
But anything meaningful for data transmission would require to operate at significant high frequencies. It's hard enough to wiggle around some "condensed energy", i.e. mass in the milligram scale at high frequencies, although in the lasers I build, the end facets of the optical filter are thrown around with accelerations on the order of 10e6 g-ees, at ~500kHz, but the gravitational waves created by that wouldn't register at LIGO even if several thousand of these, running in phase were placed right next to the test masses.
To make any sensible use of gravitational waves, we'd need to invent some form of gravitational …aser (light: laser / microwaves: maser), i.e. a gwaser. Gravitational Wave Amplification by Stimulated Emission of Radiation. Okay, I admit it, this is one of these gedankenexperiments I play through in my head from time to time, trying to come up with some technological setup, that could do it. If I had to make a bet, I'd say whatever it'd be, it'd be similar to a free electron laser.
But it's foolish to even go further than rough speculation, what components it possibly may involve, because to really make headway in that direction, we'd need a workable quantum theory of gravity. And last time I've checked, that's still an open problem.
On the uphand, should we ever figure out, if one can, and if so how to build a gwaser, this would open up possibilities far beyond new modes of communication. I'm talking propulsion that uses gravitational radiation as "reaction mass" (that'd be a no brainer, since gravitational waves to carry momentum, that's why the orbits of binary black hole systems decay in the first place). But maybe even stuff that's really outlandish science fiction, maybe even not causality breaking (not all timelike curves do violate causaility; go ahead, draw a few Minkowsky diagrams, to see what I mean) FTL travel.
And given that, I'd put this mathematical result into the same category of applicability as the Alcubierre metric: A nice consequence of mathematical rigor, but without further understanding of fundamental physics of little practical interest, so far.