They cannot shut down a private non-profit. I think you’re mistaken.
The argument has been raised for years, back in the days when there was a FR Media Chapter, it was debated endlessly
in the final analysis, NPR is protected by rows and rows of sand bags and coils of barbed wire, land mines and machine guns. In short, NPR is but a minor irritant and not worth the effort to destroy with a charge of the Light Brigade. NPR is a provider to the state stations
You also seem to not understand the nature of Public Radio. It is a function of the states that own all but stations mostly in California. A governor could force anything and let them bitch while it drags on for ever in court.