All Consequences come from the same pool unless stated otherwise (like the bonus one from getting Superb in a skill). The basic idea is that, narratively they represent how much bad stuff in aggregate the character can endure, while mechanically, being harmed in one sphere needs to have impact on other or a lot of the stuff going on becomes meaningless to many characters, so it makes sense narratively and is mechanically necessary.
Additionally, from a realism perspective, having a sprained ankle makes social interaction slightly more difficult (since you're hurting and irritable, or high on pain meds, take your pick), and people who are terribly embarrassed tend to be not at their best in a fight. Which makes it make a decent amount of sense.