I know that assembly costs for a BGA package can run into about 200-300USD for prototypes. But how important is this cost when planning a production run? Is every BGA package soldered onto the PCB actually put into an XRAY and tested? Is there any pictures showing BGA vs TQFP assembly costs for a run of about 10,000 pieces?
BGAs have superior reflow characteristics as they are pulled onto the pad during reflow (due to surface tension). Due to this effect, the placement accuracy for a BGA is slightly looser than for standard SMD components such as QFP and QFN.
QFP devices will solder wherever they have been placed.
BGAs are not a cure-all, of course; they have their challenges, particularly X-Ray post soldering, but I have had automated X-Ray testing on boards in the past that had a very low error rate.
QFP devices can catch the unwary if the PCB is tested by bed of nails or roving probe: I have seen devices where a pin was clearly not soldered, but the probe pushed it onto the pad, making an electrical contact during automated test only; the board failed a functional test, but as that is further down the process, it becomes more expensive to fix, under some circumstances.
In production, the cost of manufacturing is the cost of a pick and place which should be comparable for QFP and BGA devices on any modern system.
That is the price of hand-soldering.
If you need to hand-solder BGA during prototyping, something went wrong. You'd normally use a small reflow oven to solder the BGA ICs and any other SMD components on your prototype. If the prototype doesn't work, it is usually cheaper to build another one and throw out the components, except for some that are very expensive (e.g. it makes sense to salvage a $5000 component with 1100 pins, but you'd throw away a $50 component with 100 pins).