For the most part, responses to the thread have been very positive, so I am going to take some time to point out some of the negatives in order to push the discussion forward.
Blizzard's views on cross-faction trade
While I can't speak directly for Blizzard, I view the evidence differently than Mileiamh does. I feel that Blizzard has taken steps to purposely make some items available only to one faction, or the other. While they can be traded in neutral cities, many players may never even learn of a certain item's existence, making it rare, and therefore more intriguing, especially for collectors and completists.
I also think that as these auction houses are out of the way, and cost so much more to use, this is Blizzard's way of keeping control of cross-faction trade. I don't see why they would completely reverse the situation and encourage cross-faction auctions to equal or take over the usual means of trade.
The solution to "bad economies"
Combining two economies, which are separate entities, would not be the miracle solution that it would appear to be on the surface. If both factions had more supply than demand for cut gems, for example, combining their economies would still lead to more supply than demand.
For any given item, competition could rise steeply. You may have already seen how one tailor on your server can ruin the market for bags. This problem would be compounded, and prices could fall.
For many items, supply and demand, and therefore prices, would stay about the same. For every marketable item that grew in demand, others would fall, and the economy could, in many ways, balance out.
In addition, not every profession translates across the auction house. While enchanters could sell materials, they would still have only their own faction for selling enchants.
The lore logic
Although the alliance and horde have some areas in which they have a semi-truce (Shattrath, for example), they are ultimately at war. It makes no sense to me that my skinner and leatherworker would be working his butt off, paying to level a skill, and spending hours to gather skins, in order for the other faction to then buy them at cheap prices and make armor to protect against me. Nor do I see why blacksmiths would pay to level a skill that would help their enemies forge and wield weapons against them.