Your main comparison seems to be with CC spending and only in Amex's everyday spend categories. As an alternative, the Amex SPG card gives 1 SPG point per dollar, and 20k SPG points converts to 25k AA miles (after the 5k bonus). In some ways this is more flexible than your HH Amex approach (convert to miles so can combine flown miles and CC miles for awards; can use for upgrades; earn on all spending, not just a few categories), in some ways less flexible (in general award availability is worse than S availability).

I would say if you earn HH anyway, then maybe it's worth it. If you don't, there are better options.