This may be just a crazy idea (and I dont know if anyone has already discussed it...), but I was reading about this "inflation problem" and thought the game might be much better with some sort of financial system inside it. My idea, specifically, is to build some sort of diablo's central bank, in which you could deposit your gold in exchange for a fixed interest rate for some amount of time. This interest rate could be used to control gold inflation much like the Fed uses Fed Fund rates to control US inflation (if inflation is too high you raise interest rates, prompting players to stop "consuming new itens" in the AH for "higher savings" in the future, or you could lower interest rates if inflation was "too low" (or deflating..), prompiting players to consume now rather than in the future). The system might get even more sophisticated if blizzard used some kind of "inflation targeting", maybe defining some key item prices to be monitored (like the top legendaries, or niche itens).
The problem with this idea is that I don't trust Blizzards motivation. I believe they designed this game to be AH dependant, so that:
1 - they can get as much % as possible from RMAH transactions
2 - perhaps even covertly flood the AH with items and gold that they "generate"
3 - individual Blizzard employees could conceivably manipulate the RMAH for their personal gain
... and none of us would ever know.
Now, with regards to monitoring and trying to control inflation, in certain scenarios this could actually help Blizzard achieve their goals of cashing in on RMAH transactions, as a stable non-inflationary economy could boost RMAH use. But I honestly don't think that anyone at Blizzard is that far-sighted or logical, I think they're like a bunch of kids who just want the biggest patch in the sandbox.
As the 2nd part of kurki's post indicates, the goals of blizz RMOH and stability are actually linked(despite how cynical his post is, it's a relevant point). They do have an incentive if they realize what's good for sales, in making stable prices. Lhur's idea of a bank and interest rates, for lack of a better word, interests me. Self correcting systems to counter inflation require a lot less intervention, and under normal market conditions handle a lot better than non-self correcting systems. (the scale for interventions assumedly is the patch release schedule, though interest rates could be adjusted independently)
One significant sidenote is how a self-reacting system like that would deal with a dupe, of gold (i.e hyperinflation on steroids) or items (hyperdeflation). I haven't really thought it through, but a self-correcting system like that does weird things when overnight there's twice as much money as there was before(or the effective inverse), and those corrections may benefit those who broke the system (the last thing I want to incentivise).
Your Fed analogy is flawed in one very important way. The Fed doesn't just control the inflation by interest rates, their most powerful ability is that they can actually print money. This control over money plus interest rates helps them control inflation. The problem in D3 is that this "bank" you are proposing wouldn't control who's printing money, while you are out there trying to reduce inflation, there will be another 10000 people that are magic finding/gold finding 24/7 and in effect "print money". As long as everybody prints money your idea won't work.