Keep in mind that over-the-horizon radio communication is subject to the vagaries of the ionosphere and is not totally reliable.
Non-line-of-sight radio communications are short wave (well, also medium wave and long wave, but those modes require significant power). If ionospheric conditions are bad, as they are at many times of day (worse at night for some bands), at many times during the sunspot cycle, and during a solar storm, and sometimes during atmospheric events, then you won't get a radio signal through. One famous example of this was just prior to the Pearl Harbor attack, communications via radio between US and Hawaii were very poor or nonexistent for key parts of the time.
So to put a number to your question "likely better than half the time".
>So to put a number to your question "likely better than half the time".
I'm not sure how you get from 'because communications between arbitrary point A and and arbitrary point B are sometimes impossible on band C' that "likely better than half the time" communication will be impossible on every useful band to any useful place.
Keep in mind that over-the-horizon radio communication is subject to the vagaries of the ionosphere and is not totally reliable.
Non-line-of-sight radio communications are short wave (well, also medium wave and long wave, but those modes require significant power). If ionospheric conditions are bad, as they are at many times of day (worse at night for some bands), at many times during the sunspot cycle, and during a solar storm, and sometimes during atmospheric events, then you won't get a radio signal through. One famous example of this was just prior to the Pearl Harbor attack, communications via radio between US and Hawaii were very poor or nonexistent for key parts of the time.
So to put a number to your question "likely better than half the time".