According to my Kludge Theory of Metaphor, you'd expect that the Balls to the Wall metaphor would gain connotations from the use of the word "balls," even though that plays no part in most people's understanding of the metaphor (since they don't know its origin).
The meaning was never computed from the meanings of the word “balls” or the word “wall,” but when the network for “balls to the wall” is activated, networks associated with those words are also activated, I believe. Now, I’m an American male, which means that – outside of sports – the default meaning of “balls” is testicles. And that means “balls to the wall” is infected with the connotations of that organ, which are mainly around courage, as in “That was a ballsy move,” or “He didn’t have the balls to jump off the highest diving board.” A secondary connotation is aggression, specifically the stereotypically masculine energy and aggression that Mark Zuckerberg recently said has gone missing from tech companies like his. The way I think of it is that activating the network for “balls to the wall” activates networks related to courage, aggression, and masculinity, making those concepts more available to decision-making. Aggression is also reinforced by the connotations of motion toward a “wall.” There are thousands of TV episodes where the police push someone against a wall and frisk them in a not-gentle way. I doubt there’s more than a handful of people who don’t make that connection when they hear the lyrics to the song “Up Against the Wall Redneck Mother.”
So when someone says, “if we’re going to make this deadline, we have to go balls to the wall,” they don’t mean “we have to be thoughtful in dealing with obstacles because one of the Entailments of going faster is more risk,” and no one thinks they do. In fact, they’ll find it harder – if Lakoff is right – to even think about risk other than as something to embrace, like Real Men do.
Anecdote: the Ballsy Bull