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"might be impossible" is correct and usable in written English.
It is typically used to express uncertainty or doubt about the possibility of something. Example: It might be impossible to finish this project on time without additional help.
Exact(60)
"That same process might be impossible".
That might be impossible in 2020.
For others, it might be impossible.
The paradox might be impossible to resolve.
In fact, I'm willing to guess it might be impossible.
The speaker himself suggested agreement might be impossible.
They think it might be impossible to get".
"It might be impossible, but I should try.
But officials conceded that achieving consensus might be impossible.
The collective forces exerted by all those systems might be impossible to calculate on the fly.
Justice might be impossible in this world, but would be issued in the next.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com