By offering a prize, a large organization can "pay ahead" the cost of developing, testing, and implementing a new technology.
Look at it this way: let's assume it would cost the government $20 Billion to reduce cost-to-orbit by three-fold, say through the use of hybrid-magnetic launchers or some such. But that $20 Billion would take 20 years and dozens of missions.
Instead the agency could offer a $10 Billion prize for any company that had three successive launches at one-third the cost in the next three years. Each year after that the prize would increase by $1 Billion.
Now, instead of one technology, pursued by one agency, you have a dozen possible solutions pursued by a dozen organizations. At some point the prize money is paid out -- arguably much earlier than 20 years but who knows? It's definitely not going to cost any more money, and now you've decreased cost-to-orbit of every other mission you ever want to have. That means for every mission you have after the goal is reached, you've reduced launch costs by two-thirds.
Forever.
In addition, you're likely to end up with 3 or 4 technologies that all can reduce cost-to-orbit, all that are viable.
That's why reducing cost-to-orbit is such a critical goal. It's this huge productivity multiplier. Yes, you spend more now, but it makes all the other decisions easier (eventually). You quickly reach a point where lots of entities have the funds to do multiple missions using lots of new technologies -- a much better situation than continuing to pay more and more money for less and less return.