Bazaars, while they they can be fun, are functionally redundant and inferior to Auction Houses. Many FFXI players have come to just accept the idea, but I don't believe a game feature that encourages people to leave their game on while they aren't playing is a good one.
Not even touching on the AFK issue, it's silly to claim that bazaars are redundant or cosmetic. They serve plenty of uses.
The big one is convenience. While the auction house is set up in a major city, a bazaar can be out where it's needed. In FFXI people would sell sneak/invis potions at the entrance of dangerous areas, chocobo raising items at the chocobo stables, and crafting items at the crafting guilds. This was a valuable service.
There's also their use in featuring items. Bazaars are the billboards of the MMO world. When you check a bazaar you might find an item you'd forgotten about or never heard of before. It gives profile to items that would otherwise be buried in the AH list.
Those two advantages are the reason I suggested the "consignment" system above. One hot dog stand can reach some customers, but a chain of mobile hot dog franchises can reach many. But there are other bonuses.
They serve as an effective black market. Often people who want to get rid of items in a hurry will price them below the going rate in their bazaar so they can sell them without harming the price history. And occasionally someone who really needs an item today will buy it from a bazaar at a higher price while leaving the AH price history low so they can still buy for cheap there in the future.
And there are some other minor advantages. In FFXI, for instance, when you needed to provide several members of your party with food or something, it was easier to put them up in your bazaar than to initiate trades with everyone. And then there are the uses someone else mentioned in avoiding the restrictions of that game's AH -- taxes, item limits, unknown pricing. While those exact restrictions might not be in FFXIV's AH, you can bet that it will have some restrictions of its own.
Arguing that bazaars are inferior and therefore useless is a lot like arguing that because there's a Walmart downtown, every other store in the city is redundant.
It doesn't take very long in a Bazaar system, for certain shops to gain reputation, much like normal players gain their reputation with each other.
Oh yeah, I forgot this one. Bazaars let you establish a brand and reputation in a way that isn't possible on the semi-anonymous auction house. Edited, Jul 21st 2009 9:43am by Borkachev