I would expect it would change the feel of things, I.E. players would be less conservative with those consequences, but if that's what you're going for then I perceive no other changes. If your issue is actually with the pace then you should totally do this, but if your issue is merely with the thematic weirdness then I'd be wary, because it will change the pace.
Something that helps me is that I don't consider consequences to represent individual injuries but rather your general well-being. Consider, if you have a "Broken hand" you are pretty likely to have less energy to then argue with someone. Or if you have a "Bad reputation" it's possible that it would take a certain amount of your focus at any given time (unless you aren't the type to care about your reputation, in which case that's a pretty terrible consequence anyway) or that additional energy must be spent doing social things that would then not be there for physical conflict. Something to think about.
Also that's a very good point, it does increase the power of wizards.