The barbarian requires that you make attacks using Strength in order to get a number of benefits. This, to me, sounds very much like someone trying to enforce their personal notion of what a barbarian “should look like,” rather than a serious balance limitation. As that kind of mechanic annoys me to no end, I’d like to remove the limitation.
I realize that there might be issues with Hexblade if we open things up entirely; maybe not so bad (or no worse than Hexblade is normally), but maybe it is. Either way, that is beyond the scope of this question: the point of this question is solely opening up barbarian class features to Dex-based attacks.
So, what are the mechanical balance implications of allowing Dexterity-based attacks to benefit from barbarian class features? Primarily, does this cause Dexterity-based barbarians to overshadow the more traditional Strength-based barbarians, or do Strength-based attacks still have their niche? I don’t want to make Dexterity-based barbarians better than Strength-based ones, I just want to make them also work, ideally about equally well.