Due to the checkerboard pattern of public and private land in a lot of the US west, there are mountains that in essence are private due to the crackdown on “corner crossing”. I have a thread about this here:
One particular case I highlight is Elk Mountain in Wyoming. That mountain is nearly private since the primary private owner is shutting down corner crossing and even helicopters and planes dropping on the public sections (sections are one square mile). Here is a gifted NYTimes article about it: