I see your point, but can you make that argument in other than English? Climbing implies upward movement, for example, climbing the ladder of success. For most, the expression does not imply "failure." I feel that "climb up" is literal, while "climb down" is an oxymoron. The opposite of "climb up" is "come down."
I agree with you, rabelon. "Climb" implies an upward movement. (US English teacher, here) "Go down" or "come down" is the opposite. But I do disagree with your next statement about "climb on" and "climb on top" being the same. You can "climb but not reach the top," though you are still "climbing."
Do you mean climb into a bus? When I board a bus, I do not climb on it.