It is entirely plausible on humans.
Procedurally settled? No. And it depends on the gene of interest and its expression control mechanisms.
Safe? Not yet.
The only thing currently holding up this frontier in science is the ethical debates surrounding it.
True, but not the only thing. Attempts to put genes into bacteria, tomatoes, mice, etc do not have to worry about the failures. The individuals are expendable. The failed experiments can just go in the bin. Most effort goes into screening tests to detect the rare instances of success.
Never mind transgenic - just the technical challenges of gene therapy have ensured that progress (while real) is extremely limited, and often what worked once does not work again. Accurate delivery and integration of genes into full grown humans is far more complicated than the ethics of it.
Some progress has been made with transgenic human cell lines in culture. But again, individual cells and sub-cultures are perfectly expendable.
The future may involve culturing stem cells taken from a particular patient, doing all the trial and error work in the lab to get a gene(s) of interest into those cells and expressing correctly, screening for success and then implanting the engineered stem cells back into the human. This would be a somatic fix only - nowhere near a permanent germ line modification which is technically (and ethically) massively more problematic.