I'm assuming you're reply with the summary was meant to be totally flippant
Not totally flippant but certainly tongue in check. Yes, the question arouse from a discussion at the flight school. Collectively we couldn't find any compelling logic for a) the extra requirements for charter work and b) assuming the logic is a guard against inadvertent IMC, why the T&S rather than AH. (You would have to be very unlucky to enter IMC just as your vacuum packs it in.)
I my view, none of answers so far have really nailed why the regs are they are. The closest answer I can surmise is that the requirement goes back to days of K-S when T&S indicators were more common/affordable than AHs.