That's what HERO has done, and it's certainly interesting but not useful for most of the people who rely on USD for daily purchases (both in the United States and in other countries which peg to the dollar). We're trying to come up with something reasonable and if most merchants have goods and services they have to pay for directly, saying "this token is worth 1 USD" is the easiest approach, not a token which requires some math to figure out today's value.
In the future, as USD becomes less relevant, I'd be all about pegging to something else. Maybe a basket of currencies or SDRs or gold or silver or something. The point would be to pet to whatever most people are most comfortable using.