Every source I can find says it was a mid century phrase first found written in the 1960s from pilots. Pre aircraft locomotives would have been steam driven. Largely operated by a complex series of valves, mostly rotating so no wall to push them to. They did have a governor balanced by rotating balls, which when at full RPM would be fully extended, or: balls out.
Going balls to the wall means pushing the throttle and mixture all the way in to the firewall/instrument panel for maximum power.