I see your point, in that case it comes down to Inadvertent entry into IMC, in which case having an AH is less critical than having a T+B, as we're all taught if you enter into Inadvertent IMC then you make a 180degree turn back onto a reciprocal heading, this is done by making a rate one turn which is indicated by your T+B but not on your AH (Yes, I know you can work it out but really that's the last thing you want to be doing).
Basically for VFR Flight you shouldn't 'require' an AH for a normal flight as you are "Visual" so therefore having a regulation that requires you to have an instrument that isn't required for your normal flight wouldn't be right, but should you enter into Inadvertent IMC then you require a means of getting back out of it which is why you use your T+B to turn around not an AH. So therefore you don't REQUIRE an instrument to make a flight Visual but you DO REQUIRE an instrument to get you back to Visual.