The phrase "is otherwise impossible" is correct and usable in written English.
You can use it to indicate that something cannot be achieved or done in any other way.
Example: "Completing the project on time is otherwise impossible without additional resources."
Alternatives: "is not feasible otherwise" or "cannot be done in any other way."
He needs unity because his day job is otherwise impossible.
It is a prevalent fantasy among writers that if only one had a quiet place to work, equally free of onerous responsibilities and of pleasurable diversions, one would be able to bring forth the book that it is otherwise impossible to produce.
Due to this increased activity, social media platforms provide new opportunities for research about human behavior, information diffusion, and influence propagation at a scale that is otherwise impossible.
It is proved that the electrocatalytic activity can be highly tunable by the position of metal NPs in the LbL structure, suggesting the structural dependence of charge and mass transfer between the electrolyte and the electrode, which is otherwise impossible to investigate in a simple conventional electrode fabrication method.
Here, donors don't receive the satisfaction of knowing they've helped fund some epic project that is otherwise impossible because what they're funding already exists.
It is otherwise impossible to distinguish between what was done but not reported and what was not done.
When students are logged on, educators can monitor their work in ways that are otherwise impossible.
Yes, video games empower people by projecting their consciousness into realms where they can do things that might be otherwise impossible (like, perhaps, date the girl of your dreams).
It uses the Greek stories to trick you, or your parents (few families abide by the rating system), into tolerating a level of participatory gore that would be otherwise impossible in a mass-market entertainment.
Originally, the idea was that the self-understanding that arose as a result of psychoanalysis was unique and impressive and valid because it afforded relief from symptoms that were otherwise impossible to treat.
They have made a real difference in enabling farmers to repair much of the damage caused by intensification of agriculture – bringing back birds whose populations have been devastated, such as the skylark, and in particular the rare cirl bunting, whose recovery would have been otherwise impossible.
