"plainly impossible" is a correct and usable phrase in written English.
It can be used to describe a situation or idea that is clearly not possible or believable. Example: "It was plainly impossible for Janet to have finished her project in one day, given the amount of work required."
I found myself straining to spot climbers scaling her flanks, even though this was plainly impossible given that we were still at least 30km away.
The picture of a postwar peace table, seating Churchill, Stalin, Chian-Kai-shek and little Tom Dewey on two telephone books, is plainly impossible.
They were young, educated, and both virgins on this, their wedding night, and they lived in a time when a conversation about sexual difficulties was plainly impossible.
This, it seems to me, beggars belief, and I at first struggled to understand why any government would so publicly set out to do something so plainly impossible.
It is plainly impossible for human beings ever to occupy a position from which they could observe simultaneously both their language (thought) and the mind-independent world and establish (or ascertain) the connection.
Going cold turkey is plainly impossible; the burning issue, as with anti-apartheid divestment in the past, is to dent the standing of the companies involved, and curb their vast lobbying power.
Yet such a strike would have been vastly superior to the outcome that played out -- lots of threats, no action, and a plainly impossible-to-execute disarmament deal.
It would plainly be impossible for it to function if it was held liable for every word that appeared on its site, although it might make the abuse-reporting page more prominent.
The Stoics did not expect us never to feel unpleasant sensations, which would plainly be impossible; rather, the idea was not to let such things get to us, to impact our emotional conditions.
Writing in 1886, David Dixon Porter, who had been the commander of the Mississippi River squadron, wrote that at night the signals can be so plainly read that mistakes are impossible, and a commander-in-chief can keep up a conversation with one of his vessels distant several miles, and say what is required almost as well as if he were talking to the captain in his cabin.
After years of solidifying his political machine, George finally pushed for the kind of major economic legislation that could be plainly rife with graft but impossible to stop because of his legion of underlings.
