We have harnessed and learned to generate and control sound waves, light waves, water waves, and electromagnetic waves in general. What would be needed for science to be able to generate and use gravitational waves in the same way? What would be the outcome?
The mass of fundamental particles, like the proton or electron is very very small in comparison to the charge. This means that the motion of electrons in atoms can produce significant amounts of high frequency electromagnetic radiation.
Quantum effects stop electrons from falling into the protons they orbit.
To produce and control gravitational radiation in significant amounts you would need something very small, but very massive: a microscopic pair of black holes.
Such things would be rather hard to manage. In short it is beyond any conceivable current or future technology.
To put this in perspective, consider a fifty-plus year old human whose main source of exercise for the last twenty-plus years has been walking back and forth between work and the parking spot where the person parks his or her car. Let's strap that person to a bicycle connected to a generator. The energy output of that feeble source of energy easily exceeds the feeble 200 watt gravitational waves produced by the Earth's orbit about the Sun.
Gravitation is extremely feeble compared to electromagnetism. The electrostatic repulsion between a pair of electrons is 1045 times stronger than is the gravitation attraction between a pair of electrons. Gravitational waves are in turn extremely feeble compared to gravitation itself. I mentioned the Earth's orbit about the Sun. The total mechanical energy of that orbit is about 1034 times greater than the paltry amount of energy lost due to gravitational waves.
Imagine a Kardashev level III civilization, a civilization that has learned to harness the equivalent of the energy output of an entire galaxy. Aside: Humanity isn't even at Kardashev level I. That's another few hundred years in the future. Also note that the Kardashev scale is logarithmic. Karadshev level I is near future science fiction. Kardashev level II is also in the realm of science fiction. Kardashev level III? That's beyond science fiction.
Even that Kardashev level III civilization would not harness gravitational waves. It would instead go out of their way to avoid them. A Kardashev level III civilization might, for example, intentionally feed matter to a supermassive black hole at the heart of a galaxy to make that black hole become an active galactic nucleus. The energy output of an AGN is immense, exceeding that of a normal galaxy. The gravitational waves produced by an AGN are minuscule compared to the electromagnetic output, by a factor of about 10-80 or so.