Surely the costs/benefits to everybody, including third-parties, counts. Surely the real issue is the ultimate economic efficiency of these prizes as a way to allocate our collective resources toward achieving the most collective benefit from solved problems.

To took at a totally different area, see the Google Lunar X Prize, from their FAQ:

How much will teams spend to win the Google Lunar X PRIZE?

Three centuries of history have shown that teams competing to win incentive prizes often spend more than the prize value itself. Teams in competitions such as the Orteig Prize, the Ansari X PRIZE, and the DARPA Grand Challenges have spent as much as 5 times the prize purse value to fund their entries; and expenditures of 2.5 times the prize purse value by individual teams are relatively common.

We expect that teams pursuing the Google Lunar X PRIZE will follow these historical trends. A broad range of team expenditures—from as low as $15 million to as high as $100 million—are expected. Past prizes have shown the best funded teams do not necessarily win the prize, however. We look forward to learning from our teams as they pioneer new methods to raise money and to trim costs for a lunar mission.

Obviously, you will gain many benefits (financial and non-financial) beyond the prize if you win, but I think it is safe to say that these prizes by themselves are about inspiring people, not about (direct) financial gain.