That yellow thing is the transformer that's normally used on a switching power supply, not a step down transformer. And, as for price, I already told you the deal I got on two of them by just searching around a little bit. The example I cited was simply the first one I came across on ebay; there's tons of them out there in many, many configurations and prices. Once again, these things are constant current supplies and would require a voltage regulator to keep the voltage correct for a processor circuit; maybe an extra 50 cents or so if the board doesn't already have one. The ones I have supply a constant 350ma until the load resistance drops enough to cause it to shut down. On the high side, they max out at a little over 11V and don't go any higher. Carefully hooking it to the VIN on an arduino (UNO), they seem to work fine. The problems may come when the combination of arduino and other devices need more than the 350ma and the thing shuts down. But I won't trust it until I have much more experience with it.
It's obvious that you only want to argue rather than look into possibilities for cheaper smaller devices, so get the wall wart and be happy with it; I have dozens of them and they work fine if you want that kind of thing. I also gut them and use the power supply inside directly for some projects.
However, if one wants a self contained device that just plugs into the wall and works in the smallest possible size, there may well be better solutions. That's what I'm exploring.