This suggestion betrays a fundamental misunderstanding of "supply" in supply and demand. Supply is not just the items available right now. It's also the items could be made available very rapidly. If you have a store, the stuff on your shelves available for purchase is supply, but so is the stuff in the back rooms.
In fact, restricting the number of auctions one can make can drive prices even lower. It introduces the concept of inventory turnover. Once you've maxed out your auctions, inventory space taken up by other objects you could sell is wasted space. You need your auctions to sell quickly so that you can move items out of inventory. To do this, you price items even cheaper, so that they have the highest chance of selling.
This phenomena happens in Diablo 3. Only the best items can command good prices, or are worth the possibility of not selling. Everything else must be sold off cheaply just to clear inventory space.
The only way you can increase prices for most goods is by decreasing supply, or increasing demand. Playing games with the structure of transactions rarely works out as expected.
The only reason to have limits on the number of auctions is to limit the load on your auction house servers. If your servers can at all handle the strain, you're better off allowing as many auctions as possible.